Using Fermat’s Little Theorem, it can be shown that Σmi=1 i m−1 ≡ −1 (mod m) if m is prime. It has been conjectured that the converse is true as well. Namely, that Σmi=1 i m−1 ≡ −1 (mod m) only if m is prime. We shall present some necessary and sufficient conditions for the conjecture to hold, and we will demonstrate that no counterexample exists for m ≤ 1012 .
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-1177 |
| Date | 13 May 2008 |
| Creators | Clark, John |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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