Question

prove that x and y are odd positive integers then x^2+y^2 is even but not divisible by 4

Answer 1

we know any odd positive integer is of the form 2q+1 for any integer q. x=2m+1,y=2n+1 both are odd positive integer for any integer m,n. according to question x2+y2=(2m+1)sq.+(2n+1)sq. , 4msq.+4m+1+4nsq.+4n+1. next step take 4 as a common then answer is (Msq.+Nsq.+M+n) 2 then x2+y2 is not divided by 4