Every completely multiplicative coloring of the positive integers with values in a finite cyclic group has infinitely many monochromatic Pythagorean triples, and the unavoidable threshold is finite for every modulus.
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Standard morphisms and Pythagorean triples
Every completely multiplicative coloring of the positive integers with values in a finite cyclic group has infinitely many monochromatic Pythagorean triples, and the unavoidable threshold is finite for every modulus.