Prove that if x and y are odd positive integer, x^2+y^2 is even but not divisible by 4
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Answer: We know that any odd positive integer is of the form 2q+1, where q is an integer. So, let x=2m+1 and y=2n+1, for some integers m and n. x2+y2 is even and leaves remainder 2 when divided by 4. x2+y2 is even but not divisible by 4.
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