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## Homework Statement

Prove "The square of any integer has the form 4k or 4k+1 for some integer k.

## Homework Equations

definition of even= 2k

definition of odd= 2k+1

## The Attempt at a Solution

Basically I have: Case 1. 2k(2k) = 4k

Case 2. 2k+1(2k+1) = 4k

^{2}+4k+1 = 4k+1(k+1)

Not sure if it's correct. Do I need to use different indices? I feel I am missing something. Thanks for any help!