EGGS, squares and integer points on hyperelliptic curves

Abstract: Erdos, Graham and Selfridge considered, for each positive integer n, the least value of $t_n$ so that the integers $n+1, n+2,\ldots, n+t_n$ contain a subset the product of whose members with $n$ is a square. An open problem posed by Granville concerns the size of $t_n$ under the assumption of the ABC Conjecture. We discuss recent work, joint with Kyle Pratt and Alexandru Zaharescu, in which we establish some results on the distribution of $t_n$, including an unconditional resolution of Granville's problem.

number theory

Audience: researchers in the topic

London number theory seminar

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