Jason Adams, Nathan Jewkes and Tyrell Vance, Southern Utah University
Mathematical Sciences
We will study the divisibility of p^(n)-1 where p is a prime number larger than 5 and n is a positive integer. We will generalize the result by considering the case where n is odd and two cases where n is even. We show that when n=2^(k), k an integer greater than 1, 2^(k+2)∙3∙5 is a factor of p^(n)-1. We also show that when n=2^(m)∙l for m a positive integer greater than 1 and l an odd positive integer greater than 1, 2^(m+2)∙3∙5 is a factor of p^(n)-1.