This report focuses on the discovery of Fermat numbers as well as the subsequent innovations in processes for finding factors of Fermat numbers. The property of the prime factors of Fermat numbers, as well as the connections between Fermat numbers and other areas of mathematics, is also discussed. / text

Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.