Diophantine Equations

Although Diophantine equations provide classic examples of undecidability, the Wolfram Language in practice succeeds in solving a remarkably wide range of such equationsautomatically applying dozens of often original methods, many based on the latest advances in number theory.

ReferenceReference

FindInstance find particular solutions to Diophantine equations

Reduce general reduction of Diophantine equations and inequalities

IntegerPartitions partitions of an integer

FrobeniusSolve solve Frobenius equations

SquaresR  ▪  PowersRepresentations  ▪  PartitionsP  ▪  ...

ChineseRemainder solve simultaneous linear congruences

MultiplicativeOrder  ▪  PowerMod  ▪  ...

Minimize, Maximize integer optimization