{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:55:32Z","timestamp":1758477332204},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T00:00:00Z","timestamp":1070409600000},"content-version":"unspecified","delay-in-days":32,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2003,11]]},"abstract":"<jats:p>A classical result of S\u00e1rk\u00f6zy states that, for any <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005753_inline1.png\" \/> and any positive density subset <jats:italic>E<\/jats:italic> of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005753_inline2.png\" \/>, there exist elements <jats:italic>x<\/jats:italic> and <jats:italic>y<\/jats:italic> of <jats:italic>E<\/jats:italic> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005753_inline3.png\" \/> such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005753_inline4.png\" \/>. A version of this result for finite fields is derived from a recent theorem of P. Larick, a short proof of which is also given.<\/jats:p>","DOI":"10.1017\/s0963548303005753","type":"journal-article","created":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T14:23:14Z","timestamp":1070461394000},"page":"643-651","source":"Crossref","is-referenced-by-count":2,"title":["A S\u00e1rk\u00f6zy Theorem for Finite Fields"],"prefix":"10.1017","volume":"12","author":[{"given":"Randall","family":"McCutcheon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2003,12,3]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548303005753","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T09:22:47Z","timestamp":1589534567000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548303005753\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11]]},"references-count":0,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2003,11]]}},"alternative-id":["S0963548303005753"],"URL":"https:\/\/doi.org\/10.1017\/s0963548303005753","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,11]]}}}