Abstract
We show that if \(N \geq {\rm exp}({\rm exp}({\rm exp} (k^{O(1)})))\), then any k-colouring of the primes that are less than N contains a monochromatic solution to \(p_1 - p_2 = p_3 -1\).
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The work was conducted during the author’s DPhil study, which was supported by a Clarendon Scholarship of the University of Oxford and a Jason Hu Scholarship of Balliol College.
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Wang, R. On improving a Schur-type theorem in shifted primes. Acta Math. Hungar. 169, 216–237 (2023). https://doi.org/10.1007/s10474-023-01310-0
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DOI: https://doi.org/10.1007/s10474-023-01310-0