Q. 74.2( 72 Votes )

Prove that, if x

Answer :

Let us consider two odd positive integers x = 2m + 1 and y = 2n + 1

Then, x2 + y2 = (2m + 1)2 + (2n + 1)2


Squaring these terms using (a + b)2 = a2 + 2ab + b2


x2 + y2 = 4m2 + 1 + 4m + 4n2 + 1 + 4n


x2 + y2 = 4(m + n)2 + 4(m + n) + 2
which is even, as each term is divisible by 2

But not divisible by 4, as 3rd term is 2 which is not divisible by 4

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