Question

prove x²+y² is divisible by 2 if X and y are odd positive integers
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Answer 1

Step-by-step explanation:

As u know that sum of square of odd no. is even hence x sq. and y sq. is divisible by even

Answer 2

We know that any positive odd integer is of the form of 2q+1 where q is an integer.

Let the two odd positive number 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 sum of square is even number is divisible by 2 .

Hence, x and y are odd positive integer and x²+ y² is even and divisible by 2