\((m^2+n^2) \div (m+n)\)

\(1^2 + 2^2\) is not divisible by \(1+2.\)
\(2^2 + 3^2\) is not divisible by \(2+3.\)
\(3^2 +4^2\) is not divisible by \(3+4.\)
\(4^2 + 5^2\) is not divisible by \(4+5.\)
\(5^2 + 6^2\) is not divisible by \(5+6.\)

True or False?

If \(m\) and \(n\) are consecutive positive integers, then \(m^2 + n^2\) is never divisible by \(m+n\).

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