{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:01Z","timestamp":1753893781515,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $[z,z+3\\sqrt{z\/2}+1)$ (with $z\\geq 11$) 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 $[z,z+3\\sqrt{z\/2})$.<\/jats:p>","DOI":"10.37236\/1549","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:26Z","timestamp":1578708566000},"source":"Crossref","is-referenced-by-count":1,"title":["Product of Integers in an Interval, Modulo Squares"],"prefix":"10.37236","volume":"8","author":[{"given":"Andrew","family":"Granville","sequence":"first","affiliation":[]},{"given":"J. L.","family":"Selfridge","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,1,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:27Z","timestamp":1579324827000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1549","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,1,15]]},"article-number":"R5"}}