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Ramsey primes

For every integer \(m \geq 1\), there exists an integer \(p_0\) such that, for all primes \(p \geq p_0\), the congruence

\(x^m + y^m \equiv z^m (\mbox{mod}\ p)\)

has a solution with positive \(x\), \(y\), \(z\).

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