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- W4383604332 abstract "We present a general algorithm for solving all two-variable polynomial Diophantine equations consisting of three monomials. Before this work, even the existence of an algorithm for solving the one-parameter family of equations $x^4+axy+y^3=0$ has been an open question. We also present an elementary method that reduces the task of finding all integer solutions to a general three-monomial equation to the task of finding primitive solutions to equations with three monomials in disjoint variables. We identify a large class of three-monomial equations for which this method leads to a complete solution. Empirical data suggests that this class contains $100%$ of three-monomial equations as the number of variables goes to infinity." @default.
- W4383604332 created "2023-07-08" @default.
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- W4383604332 date "2023-07-05" @default.
- W4383604332 modified "2023-09-25" @default.
- W4383604332 title "Diophantine equations with three monomials" @default.
- W4383604332 doi "https://doi.org/10.48550/arxiv.2307.02513" @default.
- W4383604332 hasPublicationYear "2023" @default.
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