Question

Prove that, if x and y are both odd positive integers, then x2 + yz is even but not divisible by 4.​

Answer 1

Since x and y are odd positive integers so

Let x = 2n + 1 and y = 2m + 1

x² + y² = (2n + 1)² + (2m + 1)²

= 4(n² + m²) + 4(n + m) + 2

= 4 {(n² + m² + n + m}) + 2

= 4q + 2

Where q = n² + m² + n + m is an integer

Since

x² + y² is even and leaves remainder 2 when divided by 4

Not divisible by 4

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cRAZY pRINCE

Answer 2

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