Question

prove that ,if x and y are odd positive integers ,then x square +y square is even but not divisible by 4.

Answer 1

let x=5 & y=3 then sum of square of 5 & 3 is 34 which is not divisible by 4.
Hence yhe proof.

Answer 2

Step-by-step explanation:

we know that any odd positive integer is of the form 2q+1 for some integer q.

so, let x = 2m+1 and y = 2n+1 for some integers m and n.

•°• x²+y²= ( 2m+1)²+(2n+1)²

==> x²+y²=4(m²+n²)+4(m+n)+2

==> x²+y²= 4{(m²+n²)+(m+n)} +2

==> x²+y² = 4q +2 , where q= (m²+n²)+(m+n)

==> x²+y² is even and leaves remainder 2 when divided by 4.

==> x²+y² is even but not divisible by 4.

HENCE PROVED✔✔