A positive integer is of the form \( 3 q+1, q \) being a natural number. Can you write its squar...

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A positive integer is of the form \( 3 q+1, q \) being a natural number. Can you write its square in any form other than \( 3 m+1,3 m \) or \( 3 m+2 \) for some integer \( m \) ? Justify your answer.
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