Question

if x and y are two positive odd integers then prove x2+y2 is an even integer​

Answer 1

If x is an odd integer

then x^2 is a odd integer

If y is an odd integer

then y^2 is a positive odd integer

Sum of odd integers give an even no.

So sum of x^2 & y^2 is an even integer

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Answer 2

As we know that,

Sum of any ODD positive integers is always EVEN.

∴ x + y = 2a                                 ...............(  a = 1,2,3......∞, a ≥ x , y)

Now also as square of any ODD positive integers is also EVEN

∴ x² + y² = 2b                            .................( b = 1,2,3.....∞ , b ≥ x , y)

Hence proved.