{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T08:43:56Z","timestamp":1773391436401,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,4,1]],"date-time":"2012-04-01T00:00:00Z","timestamp":1333238400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s00493-012-2697-9","type":"journal-article","created":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T16:52:17Z","timestamp":1346518337000},"page":"425-449","source":"Crossref","is-referenced-by-count":23,"title":["Density and ramsey type results on algebraic equations with restricted solution sets"],"prefix":"10.1007","volume":"32","author":[{"given":"P\u00e9ter","family":"Csikv\u00e1ri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katalin","family":"Gyarmati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e1s","family":"S\u00e1rk\u00f6zy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,9,2]]},"reference":[{"key":"2697_CR1","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1073\/pnas.32.12.331","volume":"32","author":"F. Behrend","year":"1946","unstructured":"F. Behrend: On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. U. S. A. 32 (1946), 331\u2013332.","journal-title":"Proc. Nat. Acad. Sci. U. S. A."},{"key":"2697_CR2","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1007\/s000390050105","volume":"9","author":"J. Bourgain","year":"1999","unstructured":"J. Bourgain: On triples in arithmetic progressions, Geom. Funct. Anal. 9 (1999), 968\u2013984.","journal-title":"Geom. Funct. Anal."},{"key":"2697_CR3","first-page":"125","volume-title":"Number Theory, Proceedings of the First Conference of the Canadian Number Theory Association (held at Banff Center, Banff, Alberta, April 17\u201327, 1988)","author":"P. Erd\u00f6s","year":"1990","unstructured":"P. Erd\u00f6s and A. S\u00e1rk\u00f6zy: On a conjecture of Roth and some related problems, II, in: Number Theory, Proceedings of the First Conference of the Canadian Number Theory Association (held at Banff Center, Banff, Alberta, April 17\u201327, 1988), ed. R. A. Mollin, Walter de Gruyter, Berlin-New York, 1990; 125\u2013138."},{"key":"2697_CR4","series-title":"Algorithms and Combinatorics","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/978-3-642-61324-1_4","volume-title":"Irregularities of Partitions","author":"P. Erd\u00f6s","year":"1989","unstructured":"P. Erd\u00f6s, A. S\u00e1rk\u00f6zy and V. T. S\u00f3s: On a conjecture of Roth and some related problems, I, in: Irregularities of Partitions, eds. G. Hal\u00e1sz and V. T. S\u00f3s, Algorithms and Combinatorics 8, Springer-Verlag, Berlin-Heidelberg-New York, 1989; 47\u201359."},{"key":"2697_CR5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.4064\/aa97-1-3","volume":"97","author":"K. Gyarmati","year":"2001","unstructured":"K. Gyarmati: On a problem of Diophantus, Acta Arith. 97 (2001), 53\u201365.","journal-title":"Acta Arith."},{"key":"2697_CR6","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s10474-007-6192-5","volume":"118","author":"K. Gyarmati","year":"2008","unstructured":"K. Gyarmati and A. S\u00e1rk\u00f6zy: Equations in finite fields with restricted solution sets, I (Character sums), Acta Math. Hungar. 118 (2008), 129\u2013148.","journal-title":"Acta Math. Hungar."},{"key":"2697_CR7","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s10474-007-7035-0","volume":"119","author":"K. Gyarmati","year":"2008","unstructured":"K. Gyarmati and A. S\u00e1rk\u00f6zy: Equations in finite fields with restricted solution sets, II (Algebraic equations), Acta Math. Hungar. 119 (2008), 259\u2013280.","journal-title":"Acta Math. Hungar."},{"key":"2697_CR8","unstructured":"N. Hindman: Monochromatic sums equal to products in N, Integers 11A (2011), Article 10, 10."},{"key":"2697_CR9","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1112\/jlms\/s1-28.1.104","volume":"28","author":"K. F. Roth","year":"1953","unstructured":"K. F. Roth: On certain sets of integers, J. London Math. Soc. 28 (1953), 104\u2013109.","journal-title":"J. London Math. Soc."},{"key":"2697_CR10","doi-asserted-by":"crossref","first-page":"403","DOI":"10.4064\/aa118-4-6","volume":"118","author":"A. S\u00e1rk\u00f6zy","year":"2005","unstructured":"A. S\u00e1rk\u00f6zy: On sums and products of residues modulo p, Acta Arith. 118 (2005), 403\u2013409.","journal-title":"Acta Arith."},{"key":"2697_CR11","unstructured":"A. S\u00e1rk\u00f6zy: On products and shifted products of residues modulo p, Integers 8 (2008), Article 9, 8."},{"key":"2697_CR12","first-page":"114","volume":"25","author":"J. Schur","year":"1916","unstructured":"J. Schur: \u00dcber die Kongruenz x m+y m\u2261z m (mod p), Jahresber. Deutschen Math. Verein. 25 (1916), 114\u2013117.","journal-title":"Jahresber. Deutschen Math. Verein."},{"key":"2697_CR13","first-page":"212","volume":"15","author":"B. L. Waerden van der","year":"1927","unstructured":"B. L. van der Waerden: Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15 (1927), 212\u2013216.","journal-title":"Nieuw Arch. Wisk"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-012-2697-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-012-2697-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-012-2697-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T21:32:48Z","timestamp":1559079168000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-012-2697-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["2697"],"URL":"https:\/\/doi.org\/10.1007\/s00493-012-2697-9","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4]]}}}