Please write neatly and provide all the necessary steps for solving If p is an odd prime prove that np ≡ n mod 2p for all integers n .

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 33E: Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that...
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Please write neatly and provide all the necessary steps for solving

If p is an odd prime prove that np ≡ n mod 2p for all integers n .

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