= Diophantine equation
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<Polynomial> (possibly a <multivariate polynomial>) with <integer> coefficients.
Sometimes systems of <Diophantine equations> are considered.
Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.
The general problem is known to be <undecidable>: <Hilbert's tenth problem>.
The <Pythagorean triples>, and its generalization <Fermat's last theorem>, are the quintessential examples.