INTRODUÇÃO: Enquanto a análise de sobrevida tradicional estima inadequadamente o prognóstico futuro dada alguma sobrevida inicial, a sobrevida condicional ajusta a sobrevida futura pela já observada, permitindo a compreensão da distribuição temporal do impacto dos preditores. OBJETIVOS: Estimar e analisar as sobrevidas global e livre de doença até o décimo ano pós-operatório; identificar preditores independentes destes desfechos; estimar e analisar as sobrevidas condicionais global e livre de doença de cinco anos dada a sobrevida até o quinto ano pós-operatório; analisar o comportamento dos preditores dos desfechos ao longo do tempo. MÉTODOS: Estudo retrospectivo envolvendo 13 centros brasileiros. Dados clínicos, radiológicos e anatomopatológicos foram considerados. Utilizou-se o método de Kaplan-Meier com o teste log-rank para comparar fatores e a regressão de Cox obteve a razão de riscos. A sobrevida condicional foi calculada a partir das tábuas de sobrevida e a diferença padronizada reavaliou as variáveis consideradas significativas. RESULTADOS: 1157 pacientes foram incluídos. A sobrevida global de 1, 3, 5, 7 e 10 anos foi 78,6%, 72,3%, 66,0%, 61,3% e 59,4%, respectivamente. Foram preditoras de sobrevida global: idade [HR 1,04 (IC 95% 1,02-1,06), p 0.000], sexo feminino [HR 1,35 (IC 95% 1,02-1,79), p 0.038], recidiva pós-operatória do CHC [HR 1,35 (IC 95% 1,08-1,79), p 0.003], diâmetro do maior nódulo viável no explante [HR 1,01 (IC95% 1,01-1,02), p 0.006], invasão vascular não discriminada [HR 3,18 (IC95% 1,48-6,85), p 0.004], invasão micro [HR 1,65 (IC 95% 1,27-2,15), p 0.001] e macrovascular [HR 2,25 (IC 95% 1,30-3,89), p 0.000]. A sobrevida condicional global de 5 anos ao final do 1°, 3° e 5° anos foi 79,5%, 82,2% e 90,0%, respectivamente. As variáveis preditoras na análise univariada tiveram comportamento errático ao longo do tempo. A sobrevida atuarial livre de doença em 1, 3, 5, 7 e 10 anos foi 94,2%, 90,1%, 89,8%, 87,5% e 87,5%, respectivamente. Foram preditoras de sobrevida livre de doença: nível sérico de alfa-fetoproteína no diagnóstico [HR 1,0 (IC 95% 1,01-1,02), p 0.000], CHC dentro do critério de Milão no diagnóstico [HR 0,42 (IC 95% 0,22-0,80), p 0.008], explante dentro do critério de Milão [HR 0,34 (IC 95% 0,17-0,68), p 0.002], explante com neoplasia pouco diferenciada ou hepatocolangiocarcinoma [HR 3,04 (IC 95% 1,75-5,30), p 0.000], invasão vascular não discriminada [HR 15,72 (IC 95% 3,44-71,83), p 0.000], invasão micro [HR 3,40 (IC 95% 1,83-6,28), p 0.000] e macrovascular [HR 11,96 (IC 95% 5,20-27,47), p 0.000]. A sobrevida condicional livre de doença de 5 anos ao final do 1°, 3° e 5° anos foi 94,1%, 97,1% e 97,4%, respectivamente. Variáveis preditoras na análise univariada em geral tem maior impacto no primeiro ou segundo ano. CONCLUSÕES: Os resultados do transplante no Brasil foram comparáveis àqueles observados nos EUA e Europa. Considerando-se as perdas precoces, as curvas de sobrevida pelo método Kaplan-Meier foram pessimistas e a análise de sobrevida condicional fornece outra perspectiva para estes dados. O comportamento das variáveis determinantes de prognóstico não é uniforme ao longo do tempo / INTRODUCTION: Traditional survival analysis provides inadequate estimates of the future prognosis for patients with accrued survival. Conversely, conditional survival adjusts future survival by the already accrued survival. It provides insights into the temporal distribution of the effect of predictors. OBJECTIVES: To estimate and to analyse overall and disease free survival until the 10th post-operative year; to identify independent predictors of these outcomes; to estimate and to analyse 5-year overall and disease free conditional survival until the 5th post-operative year; to analyse the behaviour of the predictors of outcomes during follow-up. METHODS: Retrospective cohort from 13 Brazilian transplantation centers. Clinical, radiological, and anatomopathological data were considered. The Kaplan-Meier method with the longrank test for the comparison of factors was applied and the Cox proportional hazards model provided the hazard ratios. Conditional survival was calculated through life tables, while differences between significative variables were reassessed by the standardized difference. RESULTS: 1157 patients were included. Overall survival in 1, 3, 5, 7 and 10 years was 78.6%, 72.3%, 66.0%, 61.3%, and 59.4%, respectively. 350 (30.3%) deaths were observed, 240 (68.6%) in the 1st year. Overall survival was independently predicted by age [HR 1.04 (95% CI 1.02-1.06), p 0.000], female sex [HR 1.35 (95% CI 1.02-1.79), p 0.038], post-operative HCC recurrence [HR 1.35 (95% CI 1.08-1.79), p 0.003], diameter of the largest viable nodule on the explant [HR 1.01 (95% CI 1.01-1.02), p 0.006], non-discriminated vascular invasion [HR 3.18 (95% CI 1.48-6.85), p 0.004], micro [HR 1.65 (95% CI 1.27-2.15), p 0.001] and macrovascular invasion [HR 2.25 (95% CI 1.30-3.89), p 0.000]. 5-year overall conditional survival at the end of the 1st, 3rd and 5th post-operative years was 79.5%, 82.2%, and 90.0%, respectively. Predictors of overall survival identified on univariate analysis presented an erratic behaviour over time. Disease free survival in 1, 3, 5, 7 and 10 years was 94.2%, 90.1%, 89.8%, 87.5%, and 87.5%, respectively. 97 (8.4%) reccurrences occurred. Disease free survival was independently predicted by serum alpha-fetoprotein upon diagnosis [HR 1.0 (95% CI 1.01-1.02), p 0.000], HCC within the Milan criteria upon diagnosis [HR 0.42 (95% CI 0.22-0.80), p 0.008], explant within the Milan criteria [HR 0.34 (95% CI 0.17-0.68), p 0.002], undifferentiated tumor or hepatocholangiocarcinoma on the explant [HR 3.04 (95% CI 1.75-5.30), p 0.000], non-discriminated vascular invasion [HR 15.72 (95% CI 3.44-71.83), p 0.000], micro [HR 3.40 (95% CI 1.83-6.28), p 0.000], and macrovascular invasion [HR 11.96 (95% CI 5.20-27.47), p 0.000]. 5-year disease free conditional survival at the end of the 1st, 3rd and 5th post-operative years was 94.1%, 97.1%, and 97.4%, respectively. Predictors of recurrence on the univariate analysis usually presented with greater impact during the 1st or 2nd post-operative year. CONCLUSIONS: Outcomes of liver transplantation in Brazil were comparable to those from the US and Europe. Survival estimates through the Kaplan-Meier method were pessimistic due to greater early losses. Conditional survival offers a different perspective for the same data. The behaviour of predictive values varies over time

Contexte : La tentative de suicide (TS) concerne 8 à 10 % des adolescents et la récidive précoce 14 à 20% des adolescents. La TS peut avoir des répercussions à long terme chez les adolescents, tant au niveau scolaire/professionnel, qu’au niveau affectif et psychique. Objectifs : 1) Décrire le devenir psychosocial des suicidants et le poids de la récidive sur ce devenir, 2) étudier l’impact du fait de ne plus être joignable par l’équipe de soins 1 an après la TS et 3) étudier les modalités de communication, le soutien social et la santé perçue des jeunes suicidants. Méthode : 1) 309 sujets ont été inclus avec une évaluation au moment du geste et à 10 ans, 2) étude de l’association du fait de ne plus être joignable par l’équipe de soins avec la récidive suicidaire chez 249 patients, 3) modalité d’utilisation des moyens de communication, perception du soutien social et santé perçue de 58 adolescents suicidants. Résultats : Devenus adultes, les jeunes suicidants ont un devenir psychosocial altéré, d’autant plus lorsqu’ils avaient récidivé durant l’année suivant le geste d’inclusion. Le fait de ne plus être joignable par les soignants un an après la TS d’inclusion majore le risque de récidive suicidaire dans les 10 ans. Chez les suicidants, l’utilisation des SMS est privilégiée pour « rester en lien » avec les proches ; soutien social et santé perçue sont évalués de manière moins positive que chez leurs pairs. Perspectives : Dans un but de prévention de la récidive, nous avons développé un dispositif de veille s’appuyant sur l’envoi de SMS qui sera évalué dans un essai randomisé contrôlé. / Background: Suicide attempt (SA) concerns 8% to 10% of adolescents and SA recurrence within the year 14% to 20% of adolescents. SA of young patients may have implications over the long term on an academic/professional level, as well as on an affective and psychic level. Objectives: 1) To describe psychosocial outcomes of SAers and the weight of recurrence on these outcomes, 2) to study the impact of losing contact with caregivers during the year following SA, and 3) to study how young SAers use means of communication, and perceive social support they receive and their health-related quality of life. Methods: Three researches were carried out on adolescent SAers. 1) 309 SAers were evaluated at time of SA and 10 years after SA, 2) study of the correlation between a loss of contact with caregivers and SA recurrence occurring between 1 to 10 years after the initial SA of 249 young patients, 3) how 58 SAers use means of communication, and perceive social support they receive and their health-related quality of life. Results: As an adult, the psychosocial situation of young SAers is impaired, especially for those who have a recurrence of SA during the year after index SA. The risk of recurrence increases in the ten years following index SA for early SAers, and in the year following index SA when contact has been lost with caregivers. SAers preferentially use SMS to “keep in touch” with relatives and they assess on a less positive note than peers their social support and health-related quality of life. Perspectives: We developed a monitoring device based on SMS sending in order to prevent SA recurrence which will be assessed through a randomized controlled clinical trial.

Orientador: Adriano Dias / Resumo: O objetivo geral deste estudo foi verificar os fatores socioeconômicos, clínicos e relacionados à organização dos serviços associados ao tempo para acesso aos tratamentos do câncer de mama. Foi realizado um estudo de coorte com 600 mulheres com diagnóstico de câncer de mama internadas para tratamento clínico e/ou cirúrgico dessa doença que realizaram o primeiro tratamento em nove hospitais públicos do Distrito Federal. Não foram incluídos casos prevalentes de câncer de mama e casos que apresentavam doença metastática identificada em exames de estadiamento antes do início do tratamento. Todas as participantes foram entrevistadas entre setembro de 2012 e setembro de 2014. Os dados clínicos foram preenchidos com dados do prontuário. Em um segundo momento, realizou-se nova revisão do prontuário e/ou contato telefônico para obter informações sobre os tratamentos após a cirurgia e evolução clínica. O seguimento das mulheres ocorreu até fevereiro de 2016. Esta pesquisa foi aprovada pelo Comitê de Ética em Pesquisa da Secretaria de Estado de Saúde do Distrito Federal pelo parecer nº 99.313. As mulheres apresentavam, em média, 53,3 anos (± 12,5) ao diagnóstico e a maioria se declarou com a cor da pele parda (46,4%), referiu ter em média 7,9 anos de estudo (± 4,6), renda familiar média de R$ 2.079,01 (± R$ 2.489,23), residir no Distrito Federal (65,8%). Dentre as mulheres que buscaram os serviços de saúde a partir da autoidentificação dos sintomas sugestivos de câncer de mama, o interv... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor

Les travaux présentés dans cette thèse concernent le développement d'un outil d'analyse multiparamétrique pour la quantification de biomarqueurs urinaires du cancer de la vessie.La première partie des travaux de recherche a pour objectif la sélection de marqueurs pour le diagnostic et la récidive des tumeurs urothéliales. Une première étude a permis l'évaluation de la sélectivité de marqueurs candidats dans des échantillons urinaires de patients atteints de cancer de la vessie. Cinq des vingt marqueurs initiaux ont été sélectionnés pour leur performance diagnostique, définissant le Panel 1 : VEGF, MMP9, IL8, PTGS2 et EN2. Une seconde étude a été réalisée afin d'évaluer le potentiel de marqueurs et de paramètres cliniques pour le diagnostic de la récidive des tumeurs urothéliales. Les échantillons urinaires évalués provenaient donc de patients présentant une récidive du cancer de la vessie et de patients ne présentant pas de récidive. Le Panel 2 a ainsi été défini, basé sur le modèle de régression multiple le plus performant. Il comprend les paramètres cliniques et moléculaires suivants : nombre de récidives antérieures, nombre de thérapies par BCG, stade de la tumeur au moment du diagnostic, CDH1, IL8, ErbB2, IL6, EN2 et VEGF.La seconde partie concerne le développement d'un test multiparamétrique pour la quantification des marqueurs sélectionnés. Il s'agit d'une plateforme automatisée, à haut-débit et sous un format de plaque de microtitration 96-puits. La méthode de quantification choisie est un immunoessai de type sandwich sous la forme de puce à protéines. Le développement de la plateforme a débuté avec le Panel 1 dont trois des cinq marqueurs (VEGF, MMP9 et IL8) ont été intégrés avec succès. Suite à la seconde étude de sélection de marqueurs, le développement de l'immunoessai multiparamétrique a été orienté vers le Panel 2. À l'exception du marqueur EN2, nécessitant une configuration d'immunoessai différente, tous les marqueurs du Panel 2 ont pu être intégrés à la plateforme / The work reported in this thesis focuses on the development of a multiplex analytical tool for the quantification of selected bladder cancer urinary biomarkers.The aim of the first part of this work is the selection of urinary biomarkers for the diagnosis and recurrence of urothelial tumors. A first study evaluated the selectivity of candidate markers in urine samples of bladder cancer patients. Five of the twenty initial markers were selected for their diagnostic performance. They define Panel 1: VEGF, MMP9, IL8, PTGS2 and EN2. A second study was then conducted to assess the potential of urinary markers and clinical parameters for the diagnosis of bladder cancer recurrence. Two types of urine samples were thus evaluated: samples from recurrent bladder cancer patients and samples from bladder cancer patients without recurrence. Panel 2 was then defined based on the best performing multivariate regression model. It includes the following clinical and molecular parameters: number of past recurrences, number of BCG therapies, tumor stage at diagnosis, CDH1, IL8, ErbB2, IL6, EN2 and VEGF.The second part involves the development of a multiplex test for the quantification of the selected markers. It is a high-throughput automated platform in a 96-well microtiter plate format. It was designed as a multiplex sandwich immunoassay based on a protein microarray. The platform development began with Panel 1 for which three of the five markers (VEGF, MMP9 and IL8) were successful integrated into a multiplex immunoassay. The end of the second marker selection study marked the development transition from Panel 1 to Panel 2. With the exception of EN2, requiring a different immunoassay configuration, all the Panel 2 markers were integrated into the platform

No description available.

關於錯排列(Derangements)│D_n│=n│D_n-1│+(-1)ⁿ 的證明可用代數方法證出，甚至│D_n│的個數亦可由生成函數求出，因此我們希望能藉用更直接的觀點加以探討和證明，並找出彼此的對應。 　　當我們確定了D_n→n D_n-1的對應方式，它可以做為密碼的利用，當我們傳送一個D_n中的碼，可由譯碼的過程（即對應方式），對應到D_n-1中的一個碼（而且是1對1），因此在機密性方面有很大的幫助。 　　本文章節安排如下： 　　第一章錯排列的簡介 　　第二章如何製造錯排列 　　第三章錯排列的對應

當我們解一個遞迴關係的特徵方程式時，不管解得的根是相異根或者是重根，皆視這些跟產生的解之線性獨立為理所當然，因此很容易寫出此遞迴關係的通解乃是這些解的線性組合。在本文中，我們將透過廣義的范德蒙行列式(Generalized Vandermonde Determinant)的計算，很清楚地看出這些解之間的線性獨立。 / When we solve a characteristic equation of a recurrence relation, no matter what the roots are distinct or not, we take the linear independence of these solutions producing by each root for granted. Basing on this fact, we can easily write out the general solutions of this recurrence relation by using linear combination of these solutions. In this paper, we will see the linear independence of these solutions very clearly through the calculation of Generalized Vandermonde Determinant.

Objectives. The first aim was to examine the effects of secondary prevention with a focus on determinants in the risk of recurrent coronary heart disease (CHD). The second aim was to analyse the effects of a cognitive behavioural therapy (CBT) intervention on the risk of recurrent cardiovascular disease (CVD) and to investigate the psychosocial situation of CHD patients. Material and methods. Papers I and II were based on the Swedish Acute Myocardial Infarction Statistics Register, 1969 to 2001: 775,901 events in 589,341 subjects. Papers III and IV were based on The Secondary Prevention in Uppsala Primary Care project (SUPRIM), a randomized controlled clinical trial in 362 CHD patients. Results. The risk of a recurrent acute myocardial infarction (AMI) event was highly dependent on time from the previous event, with the greatest risk immediately after an AMI event. In addition, sex, age, and AMI number influenced the general risk level. Furthermore, there has been a major decline in recurrence risk over 30 years, and there were considerable geographical differences in risk, best explained by residential area population density, with a high recurrent AMI risk in areas with the lowest and the highest population densities, and the lowest risk in areas with moderate population density. Disease status and sex were determinants of psychological well-being the first year after a CHD event. Sex seemed to be the stronger determinant. The CBT intervention focused on stress management during one year in patients with CHD.  There was significantly improved outcome in the intervention group on recurrent CVD and recurrent AMI during a 9 year follow up. A dose-response relationship was demonstrated between attendance rate at intervention group meetings and outcome, the higher the attendance rate the better the outcome. Conclusions. The risk of a recurrent AMI event was dependent on time from the previous event, with major improvement seen in recent decades. Regional differences were best explained by population density. Female CHD patients were at high risk concerning well-being after a coronary event, which deserves special attention. The CBT intervention for CHD patients improved outcomes concerning the risk of recurrent CVD and AMI events.

In 1878, Lucas \cite{lucas} investigated the sequences $(\ell_n)_{n=0}^\infty$ where $$\ell_n=\frac{\alpha^n-\beta^n}{\alpha-\beta},$$ $\alpha \beta$ and $\alpha+\beta$ are coprime integers, and where $\beta/\alpha$ is not a root of unity. Lucas sequences are divisibility sequences; if $m|n$, then $\ell_m|\ell_n$, and more generally, $\gcd(\ell_m,\ell_n)=\ell_{\gcd(m,n)}$ for all positive integers $m$ and $n$. Matijasevic utilised this divisibility property of Lucas sequences in order to resolve Hilbert's 10th problem. \noindent In 1930, Lehmer \cite{lehmer} introduced the sequences $(u_n)_{n=0}^\infty$ where \begin{eqnarray*} u_n& = & \frac{\alpha^{n}-\beta^n}{\alpha^{\epsilon(n)}-\beta^{\epsilon(n)}},\\ \epsilon(n)&=&\left\{\begin{array}{ll} 1, \hspace{.1in}\mbox{if}\hspace{.1in}n\equiv 1 \pmod 2;\\ 2, \hspace{.1in}\mbox{if}\hspace{.1in}n\equiv 0\pmod 2;\end{array}\right. \end{eqnarray*} $\alpha \beta$ and $(\alpha +\beta)^2$ are coprime integers, and where $\beta/\alpha$ is not a root of unity. The sequences $(u_n)_{n=0}^\infty$ are known as Lehmer sequences, and the terms of these sequences are known as Lehmer numbers. Lehmer showed that his sequences had similar divisibility properties to those of Lucas sequences, and he used them to extend the Lucas test for primality. \noindent We define a prime divisor $p$ of $u_n$ to be a primitive divisor of $u_n$ if $p$ does not divide $$(\alpha^2-\beta^2)^2u_3\cdots u_{n-1}.$$ Note that in the list of prime factors of the first $n-1$ terms of the sequence $(u_n)_{n=0}^\infty$, a primitive divisor of $u_n$ is a new prime factor. \noindent We let \begin{eqnarray*} \kappa& = & k(\alpha \beta\max\{(\alpha-\beta)^2,(\alpha+\beta)^2\}),\\ \eta & = & \left\{\begin{array}{ll}1\hspace{.1in}\mbox{if}\hspace{.1in}\kappa\equiv 1\pmod 4,\\ 2\hspace{.1in}\mbox{otherwise},\end{array}\right. \end{eqnarray*} where $k(\alpha \beta \max\{(\alpha-\beta)^2,(\alpha+\beta)^2\})$ is the squarefree kernel of $\alpha \beta \max\{(\alpha-\beta)^2,(\alpha+\beta)^2\}$. On the one hand, building on the work of Schinzel \cite{schinzelI}, we prove that if $n>4$, $n\neq 6$, $n/(\eta \kappa)$ is an odd integer, and the triple $(n,\alpha,\beta)$, in case $(\alpha-\beta)^2>0$, is not equivalent to a triple $(n,\alpha,\beta)$ from an explicit table, then the $n$th Lehmer number $u_n$ has at least two primitive divisors. Moreover, we prove that if $n\geq 1.2\times 10^{10}$, and $n/(\eta \kappa)$ is an odd integer, then the $n$th Lehmer number $u_n$ has at least two primitive divisors. On the other hand, building on the work of Stewart \cite{stewart77}, we prove that there are only finitely many triples $(n,\alpha,\beta)$, where $n>6$, $n\neq 12$, and $n/(\eta \kappa)$ is an odd integer, such that the $n$th Lehmer number $u_n$ has less than two primitive divisors, and that these triples may be explicitly determined. We determine all of these triples $(n,\alpha,\beta)$ up to equivalence explicitly when $6<n\leq 30$, $n\neq 12$, and $n/(\eta \kappa)$ is an odd integer, and we tabulate the triples $(n,\alpha,\beta)$ we discovered, up to equivalence, for $30<n\leq 500$. Finally, we show that the conditions $n>6$, $n\neq 12$, are best possible, subject to the truth of two plausible conjectures.

In 1878, Lucas \cite{lucas} investigated the sequences $(\ell_n)_{n=0}^\infty$ where $$\ell_n=\frac{\alpha^n-\beta^n}{\alpha-\beta},$$ $\alpha \beta$ and $\alpha+\beta$ are coprime integers, and where $\beta/\alpha$ is not a root of unity. Lucas sequences are divisibility sequences; if $m|n$, then $\ell_m|\ell_n$, and more generally, $\gcd(\ell_m,\ell_n)=\ell_{\gcd(m,n)}$ for all positive integers $m$ and $n$. Matijasevic utilised this divisibility property of Lucas sequences in order to resolve Hilbert's 10th problem. \noindent In 1930, Lehmer \cite{lehmer} introduced the sequences $(u_n)_{n=0}^\infty$ where \begin{eqnarray*} u_n& = & \frac{\alpha^{n}-\beta^n}{\alpha^{\epsilon(n)}-\beta^{\epsilon(n)}},\\ \epsilon(n)&=&\left\{\begin{array}{ll} 1, \hspace{.1in}\mbox{if}\hspace{.1in}n\equiv 1 \pmod 2;\\ 2, \hspace{.1in}\mbox{if}\hspace{.1in}n\equiv 0\pmod 2;\end{array}\right. \end{eqnarray*} $\alpha \beta$ and $(\alpha +\beta)^2$ are coprime integers, and where $\beta/\alpha$ is not a root of unity. The sequences $(u_n)_{n=0}^\infty$ are known as Lehmer sequences, and the terms of these sequences are known as Lehmer numbers. Lehmer showed that his sequences had similar divisibility properties to those of Lucas sequences, and he used them to extend the Lucas test for primality. \noindent We define a prime divisor $p$ of $u_n$ to be a primitive divisor of $u_n$ if $p$ does not divide $$(\alpha^2-\beta^2)^2u_3\cdots u_{n-1}.$$ Note that in the list of prime factors of the first $n-1$ terms of the sequence $(u_n)_{n=0}^\infty$, a primitive divisor of $u_n$ is a new prime factor. \noindent We let \begin{eqnarray*} \kappa& = & k(\alpha \beta\max\{(\alpha-\beta)^2,(\alpha+\beta)^2\}),\\ \eta & = & \left\{\begin{array}{ll}1\hspace{.1in}\mbox{if}\hspace{.1in}\kappa\equiv 1\pmod 4,\\ 2\hspace{.1in}\mbox{otherwise},\end{array}\right. \end{eqnarray*} where $k(\alpha \beta \max\{(\alpha-\beta)^2,(\alpha+\beta)^2\})$ is the squarefree kernel of $\alpha \beta \max\{(\alpha-\beta)^2,(\alpha+\beta)^2\}$. On the one hand, building on the work of Schinzel \cite{schinzelI}, we prove that if $n>4$, $n\neq 6$, $n/(\eta \kappa)$ is an odd integer, and the triple $(n,\alpha,\beta)$, in case $(\alpha-\beta)^2>0$, is not equivalent to a triple $(n,\alpha,\beta)$ from an explicit table, then the $n$th Lehmer number $u_n$ has at least two primitive divisors. Moreover, we prove that if $n\geq 1.2\times 10^{10}$, and $n/(\eta \kappa)$ is an odd integer, then the $n$th Lehmer number $u_n$ has at least two primitive divisors. On the other hand, building on the work of Stewart \cite{stewart77}, we prove that there are only finitely many triples $(n,\alpha,\beta)$, where $n>6$, $n\neq 12$, and $n/(\eta \kappa)$ is an odd integer, such that the $n$th Lehmer number $u_n$ has less than two primitive divisors, and that these triples may be explicitly determined. We determine all of these triples $(n,\alpha,\beta)$ up to equivalence explicitly when $6<n\leq 30$, $n\neq 12$, and $n/(\eta \kappa)$ is an odd integer, and we tabulate the triples $(n,\alpha,\beta)$ we discovered, up to equivalence, for $30<n\leq 500$. Finally, we show that the conditions $n>6$, $n\neq 12$, are best possible, subject to the truth of two plausible conjectures.