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3 divides p^{2m+1}+q^{2m+1}

Source:

October 4, 2010

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Problem Statement

(MON 4)

Let

p

and

q

be two prime numbers greater than

3.

Prove that if their difference is

2^n

, then for any two integers

m

and

n,

the number

S = p^{2m+1} + q^{2m+1}

is divisible by

3.