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Creating Decidable Diophantine Equations
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DOI：10.1080/00029890.2025.2555161.png)
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Abstract
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Hilbert's famous 10th problem asked whether an algorithm exists to determine if a given Diophantine equation has a solution-in other words whether Diophantine equations are decidable. Yuri Matiyasevich proved that the answer is no, Diophantine equations are not decidable. However, it turns out that Matiyasevich's ideas can be turned around and used to construct families of decidable Diophantine equations. All you need (to get started) are the Tribonacci numbers and a bit of calculus.
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