# Combinatorial and Computational Number Theory

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(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).

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NUMBER THEORY

COMBINATORIAL AND COMPUTATIONAL NUMBER THEORY

Written by:- Thokchom Sarojkumar Sinha

(1) Prove that if g.c.d.(n,p) = 1,then pï£¦np-1 -1

Solution:- We have from Fermat's Little Theorem that

pï£¦np - n where p is a prime and n is a positive integer

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#### Solution Summary

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.