{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:50:46Z","timestamp":1740124246939,"version":"3.37.3"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,11,30]],"date-time":"2019-11-30T00:00:00Z","timestamp":1575072000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,30]],"date-time":"2019-11-30T00:00:00Z","timestamp":1575072000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 11501052"],"award-info":[{"award-number":["No. 11501052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s10998-019-00302-4","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T11:02:09Z","timestamp":1575284529000},"page":"138-144","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Diophantine equation with the harmonic mean"],"prefix":"10.1007","volume":"80","author":[{"given":"Yong","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deyi","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,30]]},"reference":[{"key":"302_CR1","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1016\/S0019-3577(07)80059-0","volume":"18","author":"MA Bennett","year":"2007","unstructured":"M.A. Bennett, The diophantine equation $$(x^k-1)(y^k-1)=(z^k-1)^t$$. Indag. Mathem. 18, 507\u2013525 (2007)","journal-title":"Indag. Mathem."},{"key":"302_CR2","volume-title":"Number Theory, Vol. I: Tools and Diophantine Equations, Graduate Texts in Mathematics","author":"H Cohen","year":"2007","unstructured":"H. Cohen, Number Theory, Vol. I: Tools and Diophantine Equations, Graduate Texts in Mathematics, vol. 239 (Springer, New York, 2007)"},{"key":"302_CR3","unstructured":"I. Connell, Elliptic curve handbook. http:\/\/www.math.mcgill.ca\/connell\/. 1998. or https:\/\/pendientedemigracion.ucm.es\/BUCM\/mat\/doc8354.pdf"},{"key":"302_CR4","first-page":"24","volume":"20","author":"LC Eggan","year":"1982","unstructured":"L.C. Eggan, P.C. Eggan, J.L. Selfridge, Polygonal products of polygonal numbers and the Pell equation. Fibonacci Quart. 20, 24\u201328 (1982)","journal-title":"Fibonacci Quart."},{"key":"302_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-26677-0","volume-title":"Unsolved Problems in Number Theory","author":"RK Guy","year":"2004","unstructured":"R.K. Guy, Unsolved Problems in Number Theory, 3rd edn. (Springer, New York, 2004)","edition":"3"},{"key":"302_CR6","first-page":"9","volume":"40","author":"S Katayama","year":"2006","unstructured":"S. Katayama, On the Diophantine equation $$(x^2+1)(y^2+1) = (z^2+1)^2$$. J. Math. Univ. Tokushima 40, 9\u201314 (2006)","journal-title":"J. Math. Univ. Tokushima"},{"key":"302_CR7","volume-title":"Diophantine Equations","author":"LJ Mordell","year":"1969","unstructured":"L.J. Mordell, Diophantine Equations (Academic Press, London, 1969)"},{"key":"302_CR8","first-page":"132","volume":"18","author":"A Schinzel","year":"1963","unstructured":"A. Schinzel, W. Sierpi\u0144ski, Sur l\u2019equation diophantienne $$(x^2-1)(y^2-1)=[((y-x)\/2)^2-1]^2$$. Elem. Math. 18, 132\u2013133 (1963)","journal-title":"Elem. Math."},{"key":"302_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4252-7","volume-title":"Rational Points on Elliptic Curves","author":"JH Silverman","year":"1992","unstructured":"J.H. Silverman, J. Tate, Rational Points on Elliptic Curves (Springer, New York, 1992)"},{"key":"302_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09494-6","volume-title":"The Arithmetic of Elliptic Curves","author":"JH Silverman","year":"2009","unstructured":"J.H. Silverman, The Arithmetic of Elliptic Curves, 3rd edn. (Springer, New York, 2009)","edition":"3"},{"key":"302_CR11","first-page":"37","volume":"22","author":"K Szymiczek","year":"1967","unstructured":"K. Szymiczek, On a diophantine equation. Elem. Math. 22, 37\u201338 (1967)","journal-title":"Elem. Math."},{"key":"302_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4064\/cm107-1-1","volume":"107","author":"M Ulas","year":"2007","unstructured":"M. Ulas, On the diophantine equation $$f(x)f(y)=f(z)^2$$. Colloq. Math. 107, 1\u20136 (2007)","journal-title":"Colloq. Math."},{"key":"302_CR13","doi-asserted-by":"publisher","first-page":"2091","DOI":"10.1216\/RMJ-2008-38-6-2091","volume":"38","author":"M Ulas","year":"2008","unstructured":"M. Ulas, On the diophantine equation $$(x^2+k)(y^2+k)=(z^2+k)^2$$. Rocky Mt. J. Math. 38, 2091\u20132097 (2008)","journal-title":"Rocky Mt. J. Math."},{"key":"302_CR14","doi-asserted-by":"publisher","first-page":"31","DOI":"10.5486\/PMD.2013.5190","volume":"82","author":"Y Zhang","year":"2013","unstructured":"Y. Zhang, T. Cai, On the Diophantine equation $$f(x)f(y)=f(z^2)$$. Publ. Math. Debr. 82, 31\u201341 (2013)","journal-title":"Publ. Math. Debr."},{"key":"302_CR15","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s10998-014-0068-6","volume":"70","author":"Y Zhang","year":"2015","unstructured":"Y. Zhang, T. Cai, A note on the Diophantine equation $$f(x)f(y)=f(z^2)$$. Period. Math. Hungar. 70, 209\u2013215 (2015)","journal-title":"Period. Math. Hungar."},{"key":"302_CR16","doi-asserted-by":"publisher","first-page":"275","DOI":"10.4064\/cm142-2-8","volume":"142","author":"Y Zhang","year":"2016","unstructured":"Y. Zhang, Some observations on the Diophantine equation $$f(x)f(y)=f(z)^2$$. Colloq. Math. 142, 275\u2013284 (2016)","journal-title":"Colloq. Math."},{"key":"302_CR17","doi-asserted-by":"publisher","first-page":"111","DOI":"10.4064\/cm6920-1-2017","volume":"151","author":"Y Zhang","year":"2018","unstructured":"Y. Zhang, On the Diophantine equation $$f(x)f(y)=f(z)^n$$ involving Laurent polynomials. Colloq. Math. 151, 111\u2013122 (2018)","journal-title":"Colloq. Math."},{"key":"302_CR18","doi-asserted-by":"publisher","first-page":"119","DOI":"10.4064\/cm7528-10-2018","volume":"158","author":"Y Zhang","year":"2019","unstructured":"Y. Zhang, A.S. Zargar, On the Diophantine equation $$f(x)f(y)=f(z)^n$$ involving Laurent polynomials. II. Colloq. Math. 158, 119\u2013126 (2019)","journal-title":"II. Colloq. Math."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-019-00302-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-019-00302-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-019-00302-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T00:32:34Z","timestamp":1606609954000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-019-00302-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,30]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["302"],"URL":"https:\/\/doi.org\/10.1007\/s10998-019-00302-4","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2019,11,30]]},"assertion":[{"value":"30 November 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}