See attached file for full problem description.
(a) Prove that if g.c.d.(n,p) = 1,then p divides n^(p-1) -1.
(b) Prove that if 3 is not a divisor of n, then 3 divides n^2 -1.
(c) Prove that if 5 is not a divisor of (n - 1), 5 is not a divisor of n,and 5 is not a divisor of (n+1), then 5 divides (n^2 + 1).
Please see the attached file.
COMBINATORIAL AND COMPUTATIONAL NUMBER THEORY
Written by:- Thokchom Sarojkumar Sinha
(1) Prove that if g.c.d.(n,p) = 1,then pnp-1 -1
Solution:- We have from Fermat's Little Theorem that
pnp - n where p is a prime and n is a positive integer
This solution is comprised of a detailed explanation for Combinatorial and Computational Number Theory. It contains step-by-step explanation for finding the solution of the problems.