Question

If X and y are odd positive integers and x² + y² is even,then x² + y² is not always divisible by

Answer 1

Answer:

Hey mate, here is your answer

Step-by-step explanation:

writing two answer both are correct

Let the two odd numbers be

(2a+1) & (2b+1) because if we add 1 to any even no. it will be odd.

x²+y²

=>(2a+1)²+(2b+1)²

=>(4a²+4a+1)+(4b²+4b+1)

=>4(a²+b²+a+b)+2

4 Is not a multiple of 2 it means clearly that 4 is not multiple of x²+y² , so x²+y² is even but not divisible by 4.

Hence proved.

or

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

thank you