{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:01:18Z","timestamp":1777366878794,"version":"3.51.4"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,1,28]],"date-time":"2016-01-28T00:00:00Z","timestamp":1453939200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1007\/s10998-016-0111-x","type":"journal-article","created":{"date-parts":[[2016,1,28]],"date-time":"2016-01-28T02:22:18Z","timestamp":1453947738000},"page":"37-42","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["The complete solution of the Diophantine equation $$(4m^2+1)^x+(5m^2-1)^y=(3m)^z$$ ( 4 m 2 + 1 ) x + ( 5 m 2 - 1 ) y = ( 3 m ) z"],"prefix":"10.1007","volume":"72","author":[{"given":"Csan\u00e1d","family":"Bert\u00f3k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,28]]},"reference":[{"key":"111_CR1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1216\/rmjm\/1181072793","volume":"22","author":"LJ Alex","year":"1992","unstructured":"L.J. Alex, L.L. Foster, On the diophatine equation $$1+x+y=z$$ 1 + x + y = z . Rocky Mt. J. Math. 22, 11\u201362 (1992)","journal-title":"Rocky Mt. J. Math."},{"key":"111_CR2","first-page":"13","volume":"8","author":"LJ Alex","year":"1995","unstructured":"L.J. Alex, L.L. Foster, On the diophatine equation $$w+x+y=z$$ w + x + y = z with $$wxyz=2^r3^s5^t$$ w x y z = 2 r 3 s 5 t . Rev. Mat. Univ. Complut. Madr. 8, 13\u201348 (1995)","journal-title":"Rev. Mat. Univ. Complut. Madr."},{"key":"111_CR3","doi-asserted-by":"crossref","unstructured":"Cs. Bert\u00f3k, L. Hajdu, A Hasse-type principle for exponential Diophantine equations and its applications. Math. Comp. 85, 849\u2013860 (2016)","DOI":"10.1090\/mcom\/3002"},{"key":"111_CR4","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2140\/pjm.1982.101.263","volume":"101","author":"JL Brenner","year":"1982","unstructured":"J.L. Brenner, L.L. Foster, Exponential Diophantine equations. Pac. J. Math. 101, 263\u2013301 (1982)","journal-title":"Pac. J. Math."},{"key":"111_CR5","doi-asserted-by":"crossref","first-page":"365","DOI":"10.4064\/aa-58-4-363-385","volume":"58","author":"P Erd\u0151s","year":"1991","unstructured":"P. Erd\u0151s, C. Pomerance, E. Schmutz, Carmichael\u2019s lambda function. Acta Arith. 58, 365\u2013385 (1991)","journal-title":"Acta Arith."},{"key":"111_CR6","unstructured":"L. Jes\u0300manowicz, Some remarks on Pythagorean numbers. Wiadom. Mat. 1, 196\u2013202 (1955\/1956)"},{"key":"111_CR7","unstructured":"W. A. Stein et al., Sage Mathematics Software (Version 6.2), The Sage Development Team, (2014), http:\/\/www.sagemath.org"},{"key":"111_CR8","doi-asserted-by":"crossref","unstructured":"J. Su, X. Li, The exponential diophantine equation $$(4m^2+1)^x+(5m^2-1)^y=(3m)^z$$ ( 4 m 2 + 1 ) x + ( 5 m 2 - 1 ) y = ( 3 m ) z . Abstr. Appl. Anal. 2014, Article ID 670175 (2014)","DOI":"10.1155\/2014\/670175"},{"key":"111_CR9","doi-asserted-by":"crossref","first-page":"22","DOI":"10.3792\/pjaa.70.22","volume":"70","author":"N Terai","year":"1994","unstructured":"N. Terai, The Diophantine equation $$a^x+b^y=c^z$$ a x + b y = c z . Proc. Jpn. Acad. Ser. A Math. Sci. 70, 22\u201326 (1994)","journal-title":"Proc. Jpn. Acad. Ser. A Math. Sci."},{"key":"111_CR10","doi-asserted-by":"crossref","first-page":"109","DOI":"10.3792\/pjaa.71.109","volume":"71","author":"N Terai","year":"1995","unstructured":"N. Terai, The Diophantine equation $$a^x+b^y=c^z$$ a x + b y = c z , II. Proc. Jpn. Acad. Ser. A Math. Sci. 71, 109\u2013110 (1995)","journal-title":"Proc. Jpn. Acad. Ser. A Math. Sci."},{"key":"111_CR11","doi-asserted-by":"crossref","first-page":"20","DOI":"10.3792\/pjaa.72.20","volume":"72","author":"N Terai","year":"1996","unstructured":"N. Terai, The Diophantine equation $$a^x+b^y=c^z$$ a x + b y = c z , III. Proc. Jpn. Acad. Ser. A Math. Sci. 72, 20\u201322 (1996)","journal-title":"Proc. Jpn. Acad. Ser. A Math. Sci."},{"key":"111_CR12","first-page":"1135","volume":"6","author":"N Terai","year":"2012","unstructured":"N. Terai, On the exponential Diophantine equation $$(4m^2+1)^x+(5m^2-1)^y=(3m)^z$$ ( 4 m 2 + 1 ) x + ( 5 m 2 - 1 ) y = ( 3 m ) z . Int. J. Algebra 6, 1135\u20131146 (2012)","journal-title":"Int. J. Algebra"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-016-0111-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-016-0111-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-016-0111-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,3]],"date-time":"2019-09-03T22:27:46Z","timestamp":1567549666000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-016-0111-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,28]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["111"],"URL":"https:\/\/doi.org\/10.1007\/s10998-016-0111-x","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,28]]}}}