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 - We thank the anonymous referee for a careful reading of the manuscript and for helpful comments. We especially thank the referee for sharing with us the proof of Theorem presented above, which is significantly shorter than our original proof. KP was supported by a post-doctoral research fellowship at All Souls College, University of Oxford, during the course of this work.
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 -