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).
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
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