What question did this study set out to answer?

To demonstrate that Hilbert's tenth problem has a negative answer in specific infinite rings over integers.

Hilbert’s tenth problem via additive combinatorics

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To demonstrate that Hilbert's tenth problem has a negative answer in specific infinite rings over integers.
Construct elliptic curves without rank growth in certain quadratic extensions.
Utilize techniques from additive combinatorics combined with 2-descent.
Established that infinite rings finitely generated over integers can lead to a negative answer for Hilbert’s tenth problem.

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Randomized trial shows a negative answer for Hilbert’s tenth problem in infinite rings, suggesting new insights in number theory.

Koymans et al. (2026) studied this question.

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