Prove that if `xa n dy` are odd positive integers, then `x^2+y^2` is even but not divisible by 4.

Explanation

To prove that if \( x \) and \( y \) are odd positive integers, then \( x^2 + y^2 \) is even but not divisible by 4, we will follow these steps:

### Step 1: Define odd integers
Let \( x \) and \( y \) be odd positive integers. By definition, any odd integer can be expressed in the form:
\[ x = 2n + 1 \quad \text{and} \quad y = 2m + 1 \]
where \( n \) and \( m \) are non-negative integers.
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