SOLUTION: x and y are integers. show that x^2-y^2 is odd or divisible by 4

Question 366474: x and y are integers. show that x^2-y^2 is odd or divisible by 4
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
let x be even, y even : x = 2m, y = 2n

then x^2 - y^2 = 4m^2 - 4n^2 = 4 (m^2 - n^2) which is divisible by 4

if x were odd : x = 2m + 1

x^2 - y^2 = 4m^2 + 4m + 1 + 2n^2 = 2(2m^1 + 2m + 2n^2) + 1, which is odd

if x even, y odd, we find this is odd, similar as above.

if x odd, y odd, 4m^2 + 4m + 1 - 4n^2 - 4n - 1, which is divisible by 4

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