Prove that if `x and y` are odd positive integers, then `x^2+y^2` is even but not divisible by 4.

Prove that if xa n dy are odd positive integers, then x^2+y^2 is even but not divisible by 4.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If x and y are positive integers and (2x +y) is even, which of the following must be even ?

Prove that n^2-n divisible by 2 for every positive integer n.

(x)/(8)+(y)/(5)=(31)/(40) In the equation above, if x and y are positive integers, what is the value of x+y?

If x and y are positive integers and sqrt(x) = y + 3 ,then what is the value of y^(2) ?

If x, y, and z are consecutive integers, is x+y+z divisible by 3?

Check the validity of the following statement. If x and y are odd integers, then xy is an odd integer.

Prove that the product of two consecutive positive integers is divisible by 2.