Question

prove that if x and y are both odd positive integers then x2+y2 is even but not divisible by 4

Answer 1

Let us have two odd numbers 1 and 15.
Then it becomes 1^2+15^2=1+225=226.
For divisibility of 4 the last two digits should be a multiple of 4.
Since the last two digits of 226 is 26 and it is not a multiple of 4.
HENCE PROVED