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## Homework Statement

Hello Guys, can you check my proof.

Problem statement: Let n be an integer such that n

^{2}is even. Prove that n

^{2}is divisible by 4.

Proof by contradiction:

Suppose n

^{2}is not divisible by 4, thus n is odd. Such that n=2p+1, and n

^{2}=4p

^{2}+4p+1. Factoring out 2 we have 2(2p

^{2}+2p+.5) which is even, and divisible by 4. Thus we have a contradiction. End of proof.