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Show that the square of any positive int...

Show that the square of any positive integer cannot be of the form 6m+2 or 6m+5 for some integer q.

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To show that the square of any positive integer cannot be of the form \(6m + 2\) or \(6m + 5\) for some integer \(m\), we will analyze the squares of integers based on their possible remainders when divided by 6. ### Step-by-Step Solution: 1. **Understanding the Remainders:** Any integer \(a\) can be expressed in one of the following forms based on its remainder when divided by 6: - \(a = 6m\) (remainder 0) - \(a = 6m + 1\) (remainder 1) ...
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