Question

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Answer 1

$\huge{\mathcal{ANSWER:-}}$

$\star{\texttt{GIVEN - \: x\:and\:y\:are\:odd\:integers}}$

Odd numbers are of the form 2q + 1

Let x = 2m + 1

y = 2n + 1

Now,

x²+y²

=( 2m + 1)² + (2n + 1)²

= 4m² + 4m + 1 + 4n² + 4n + 1

= 4m² + 4n² + 4m + 4n + 2

= 4 (m² + n² + m + n) + 2

= 4 k + 2 ,(where k = m²+n²+m+n)

It is a even number but not divisible by 4 since it has remainder 2