# On improving a Schur-type theorem in shifted primes

@inproceedings{Wang2021OnIA, title={On improving a Schur-type theorem in shifted primes}, author={Ruoyi Wang}, year={2021} }

We show that if N ≥ exp(exp(exp(k))), then any k-colouring of the primes that are less than N contains a monochromatic solution to p1 − p2 = p3 − 1.

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For
$$k \in \mathbb {N}$$
, write S(k) for the largest natural number such that there is a k-colouring of
$$\{1, \ldots ,S(k)\}$$
with no monochromatic solution to
$$x-y=z^2$$
. That S(k)…