Chaogui Zhang
Abstract
Let f(n) be the length of the shortest interval starting at n that contains a subset of at least two integers whose product is a perfect square. We prove that there are infinitely many n such that f(n) is subexponential (in ln n). Results on smooth integer distribution over short intervals are applied to this problem.
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Let f(n) be the length of the shortest interval starting at n that contains a subset of at least two integers whose product is a perfect square. We prove that there are infinitely many n such that f(n) is subexponential (in ln n). Results on smooth integer distribution over short intervals are applied to this problem.
Key concepts: Mathematics, Interval (graph theory), Integer (computer science), Square (algebra), Combinatorics, Product (mathematics), Square number, Discrete mathematics