Question

Prove that x and y are odd positive integers , then x2 +y2 is even but not divisible by 4

Answer 1

Answer:

Step-by-step explanation:

Let the two odd positive no. be x = 2k + 1 and y = 2p + 1

Hence, x2 + y2 = (2k + 1)2 +(2p + 1)2

                        = 4k2 + 4k + 1  + 4p2 + 4p + 1

                        = 4k2 + 4p2 + 4k + 4p + 2

                        = 4 (k2 + p2 + k + p) + 2  

clearly, notice that the sum of square is even the no. is not divisible by 4

hence, if x and y are odd positive integer, then x2 + y2 is even but not divisible by four.