Question

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

Answer 1

As x and y are odd there square is also odd thus x^2 and y^2 is also odd. And odd + odd is even thus x^2 + y^2 is even.

Answer 2

Answer:

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 integer m and n.

∴x^2+y^2=(2m+1)^2(2n+1)^2

⇒x^2+y^2=4(m^2+1)+4(m+n)+2

⇒x^2+y^2=4q=2,where q=(m^2+n^2)+(m+n)

⇒x^2+y^2 is even and leaves remainder 2 when divided by 4

∴x^2+y^2 is even but not divisible by 4