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Research Article Open access CC BY 4.0

An Example of the Application of Provability Logic to Unsolved Problems in Number Theory: The Cullen Numbers and Conway’s Supposition

Alexander Bolotin

Journal of Advances in Mathematics and Computer Science · pp. 1–5 · Published 5 Aug 2016

10.9734/BJMCS/2016/27581

Abstract

This short paper offers an example of possibly fruitful interactions between modal logic and number theory. In the paper, Conway's remark that p and p.2p + 1  can both be prime numbers is formulated as a formula of modal logic and then analyzed for its decidability.

Modal logic provability logic Fermat’s last theorem Cullen numbers Conway's remark decidability

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