MathDBNoncomputability conjecture for finite-solution Diophantine equations
Noncomputability conjecture for finite-solution Diophantine equations
Consider the collection of Diophantine equations over the rationals that have only finitely many rational solutions. Noncomputability conjecture. This collection is not computable. The source states that Harvey Friedman's stronger non-recursive-enumerability conjecture implies this claim, but does not establish either claim.
Sources & referencesView supporting material
Primary source
Apoloniusz Tyszka, “Is there a computable upper bound on the heights of rational solutions of a Diophantine equation with a finite number of solutions?”, arXiv:1511.06689 (2017).
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