Question

Hey Mates❤️
✨Here is a Difficult Question✨
Answer this❗️❗️
$Prove \: that \:if \: x \: and \: y \: are \: both \: odd \: positive \: integers \: \\ , then \: {x}^{2}+ {y}^{2} \: is \: even \: but \: not \: divisble \: by \: 4$
Thanks❤️❤️
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Answer 1

Hii mate here is Your Answer,

Given :- X and Y are odd positive integers so it can be written as follows :-

x = 2m +1 and y = 2m +1 ( format of odd no.)

=> x^2 + y^2 = (2m +1)^2 + (2m + 1)^2

=> (4m^2 + 4m + 1) + (4m^2 + 4m + 1)

=> 8m^2 + 8m + 2

•From this number only 2 can be taken common as 2( 4m^2 + 4m + 1 ) but 4 cannot be taken common.

• as it is divisible by 2 it is an even no. but not divisible by 4 .....(Ans.)