TY - JOUR

T1 - A problem of Erdős-Graham-Granville-Selfridge on integral points on hyperelliptic curves

AU - Bui, Hung M.

AU - Pratt, Kyle

AU - Zaharescu, Alexandru

N1 - Publisher Copyright:
© 2023 The Author(s). Published by Cambridge University Press on behalf of Cambridge Philosophical Society.

PY - 2024/3/5

Y1 - 2024/3/5

N2 - Erdős, Graham and Selfridge considered, for each positive integer n, the least value of so that the integers contain a subset the product of whose members with n is a square. An open problem posed by Granville concerns the size of, under the assumption of the ABC conjecture. We establish some results on the distribution of, and in the process solve Granville's problem unconditionally.

AB - Erdős, Graham and Selfridge considered, for each positive integer n, the least value of so that the integers contain a subset the product of whose members with n is a square. An open problem posed by Granville concerns the size of, under the assumption of the ABC conjecture. We establish some results on the distribution of, and in the process solve Granville's problem unconditionally.

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U2 - 10.1017/S0305004123000488

DO - 10.1017/S0305004123000488

M3 - Article

AN - SCOPUS:85174323453

SN - 0305-0041

VL - 176

SP - 309

EP - 323

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -