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- W2137608889 abstract "We prove a conjecture of Irving Kaplansky which asserts that between any pair of consecutive positive squares there is a set of distinct integers whose product is twice a square. Along similar lines, our main theorem asserts that if prime $p$ divides some integer in $[z,z+3sqrt{z/2}+1)$ (with $zgeq 11$) then there is a set of integers in the interval whose product is $p$ times a square. This is probably best possible, because it seems likely that there are arbitrarily large counterexamples if we shorten the interval to $[z,z+3sqrt{z/2})$." @default.
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- W2137608889 date "2001-01-15" @default.
- W2137608889 modified "2023-10-17" @default.
- W2137608889 title "Product of Integers in an Interval, Modulo Squares" @default.
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- W2137608889 doi "https://doi.org/10.37236/1549" @default.
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