Prove that if x and y are both odd positive intergers then ` x^(2) +y^(2) ` is even but not divisible by 5.

Prove that if x and y are both odd positive integers then x^(2) + y^(2) is even but not divisible by 4

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

Consider the following statements in respect of positive odd integers x and y : 1. x^2 +y^2 is even integer. 2. x^2+y^2 is divisible by 4. Which of the above statements is/are correct ?

Prove that if x is even then x^(2) is even

Find the number of positive intergers up to 100 which are not divisible by any 2,3 and 5 ?

Two natural numbers x and y are chosen at random. What is the probability that x^(2) + y^(2) is divisible by 5?

Prove that relation define on positive integers such as R={(x,y):x-y is divisible by 3 where x,y in N} is an equivalence relation.

If x is positive even integer and y is negative odd integer, then x^(y) is