# Diophantine equations: a systematic approach

@inproceedings{Grechuk2021DiophantineEA, title={Diophantine equations: a systematic approach}, author={Bogdan Grechuk}, year={2021} }

By combining computer assistance with human reasoning, we have solved the Hilbert’s tenth problem for all polynomial Diophantine equations of size at most 28, where the size is defined in [37]. In addition, we have solved this problem for all two-variable Diophantine equations of size at most 31, all symmetric equations of size at most 36, and all three-monomial equations of size at most 45. In each category, we identified the smallest equations for which the Hilbert’s tenth problem remains… Expand

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