Question

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

Answer 1

➡HERE IS YOUR ANSWER⬇

Let, the odd integers are

x = (2n + 1) and (2m + 3), where n belongs to the set of Natural numbers.

${x}^{2} + {y}^{2} \\ \\ = {(2n + 1)}^{2} + {(2n + 3)}^{2} \\ \\ = (4 {n}^{2} + 4n + 1) + (4 {n}^{2} + 12n + 9) \\ \\ = 8 {n}^{2} +1 6n + 10 \\ \\ = 2(4 {n}^{2} + 8n + 5)$


which is surely an even number. But it is clear that the number is not divisible by 4.

⬆HOPE THIS HELPS YOU⬅