KnowraDiophantine equationLinked fromLinked fromThe 41 pages that link to Diophantine equation, each with the reason it gives.All 41Broader topic 3Related 12Narrower topic 26FibonacciNarrower topic: Problems of integer solutions underpin the mathematical investigations in his Book of Squares.p-adic numberNarrower topic: Checking solutions over p-adic fields can constrain the rational solutions of arithmetic equations.DiophantusNarrower topic: Modern terminology honors Diophantus for his attention to equations with constrained solutions.Hermann MinkowskiNarrower topic: Minkowski’s geometric methods turn questions about integer solutions into questions about lattice points.Additive number theoryNarrower topic: Representation questions become Diophantine equations when the allowed summands are specified.Pell equationNarrower topic: The Pell equation is a classic case of an equation restricted to integer solutions.Pythagorean tripleNarrower topic: Finding triples is an integer-solution problem for a quadratic equation.Rational pointNarrower topic: Its rational solutions are rational points on the variety defined by the equation.Hilbert's tenth problemNarrower topic: These are precisely the equations whose integer solvability the problem asks an algorithm to decide.Egyptian fractionNarrower topic: Finding Egyptian fraction representations is a Diophantine problem with denominator constraints.Algebraic number fieldNarrower topic: Number fields provide tools for studying integer solutions and factoring equations.Fermat's theorem on sums of two squaresNarrower topic: The theorem answers an integer-solvability question for p=x²+y².Infinite descentNarrower topic: Descent most often rules out or classifies integer solutions to such equations.Arithmetic geometryNarrower topic: The subject generalizes classical questions about integer solutions to geometric settings.Catalan's conjectureNarrower topic: Its proof advances methods for equations requiring integer solutions.Julia RobinsonNarrower topic: Hilbert’s tenth problem asks for a uniform method to test integer solutions.abc conjectureNarrower topic: The conjecture would control solutions to many equations through their prime factors.Erdős–Straus conjectureNarrower topic: The conjecture is an infinite family of equations requiring positive-integer solutions.Fermat's right triangle theoremNarrower topic: The triangle's side lengths and square area impose simultaneous integer equations.Ramanujan–Nagell equationNarrower topic: The equation belongs to the tradition of integer-solution problems named for Diophantus.Markov numberNarrower topic: The defining equation makes Markov numbers part of an integer-solution problem.Sophie Germain's theoremNarrower topic: The theorem excludes integer solutions to a particular Diophantine equation.Beal's conjectureNarrower topic: Beal's conjecture asks what divisibility must hold for integer solutions to a power equation.Birch's theoremNarrower topic: The theorem counts integer solutions to a family of Diophantine equations.Goormaghtigh conjectureNarrower topic: The conjecture asks whether an integer equation has any solutions beyond two known cases.Tijdeman's theoremNarrower topic: Pairs of powers with a fixed difference form an integer equation.
KnowraDiophantine equationLinked fromLinked fromThe 41 pages that link to Diophantine equation, each with the reason it gives.All 41Broader topic 3Related 12Narrower topic 26FibonacciNarrower topic: Problems of integer solutions underpin the mathematical investigations in his Book of Squares.p-adic numberNarrower topic: Checking solutions over p-adic fields can constrain the rational solutions of arithmetic equations.DiophantusNarrower topic: Modern terminology honors Diophantus for his attention to equations with constrained solutions.Hermann MinkowskiNarrower topic: Minkowski’s geometric methods turn questions about integer solutions into questions about lattice points.Additive number theoryNarrower topic: Representation questions become Diophantine equations when the allowed summands are specified.Pell equationNarrower topic: The Pell equation is a classic case of an equation restricted to integer solutions.Pythagorean tripleNarrower topic: Finding triples is an integer-solution problem for a quadratic equation.Rational pointNarrower topic: Its rational solutions are rational points on the variety defined by the equation.Hilbert's tenth problemNarrower topic: These are precisely the equations whose integer solvability the problem asks an algorithm to decide.Egyptian fractionNarrower topic: Finding Egyptian fraction representations is a Diophantine problem with denominator constraints.Algebraic number fieldNarrower topic: Number fields provide tools for studying integer solutions and factoring equations.Fermat's theorem on sums of two squaresNarrower topic: The theorem answers an integer-solvability question for p=x²+y².Infinite descentNarrower topic: Descent most often rules out or classifies integer solutions to such equations.Arithmetic geometryNarrower topic: The subject generalizes classical questions about integer solutions to geometric settings.Catalan's conjectureNarrower topic: Its proof advances methods for equations requiring integer solutions.Julia RobinsonNarrower topic: Hilbert’s tenth problem asks for a uniform method to test integer solutions.abc conjectureNarrower topic: The conjecture would control solutions to many equations through their prime factors.Erdős–Straus conjectureNarrower topic: The conjecture is an infinite family of equations requiring positive-integer solutions.Fermat's right triangle theoremNarrower topic: The triangle's side lengths and square area impose simultaneous integer equations.Ramanujan–Nagell equationNarrower topic: The equation belongs to the tradition of integer-solution problems named for Diophantus.Markov numberNarrower topic: The defining equation makes Markov numbers part of an integer-solution problem.Sophie Germain's theoremNarrower topic: The theorem excludes integer solutions to a particular Diophantine equation.Beal's conjectureNarrower topic: Beal's conjecture asks what divisibility must hold for integer solutions to a power equation.Birch's theoremNarrower topic: The theorem counts integer solutions to a family of Diophantine equations.Goormaghtigh conjectureNarrower topic: The conjecture asks whether an integer equation has any solutions beyond two known cases.Tijdeman's theoremNarrower topic: Pairs of powers with a fixed difference form an integer equation.