{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T15:24:48Z","timestamp":1726413888746},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T00:00:00Z","timestamp":1625875200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T00:00:00Z","timestamp":1625875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s10998-021-00405-x","type":"journal-article","created":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T11:02:22Z","timestamp":1625914942000},"page":"287-298","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A purely exponential Diophantine equation in three unknowns"],"prefix":"10.1007","volume":"84","author":[{"given":"Takafumi","family":"Miyazaki","sequence":"first","affiliation":[]},{"given":"Masaki","family":"Sudo","sequence":"additional","affiliation":[]},{"given":"Nobuhiro","family":"Terai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,10]]},"reference":[{"key":"405_CR1","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1090\/mcom\/3002","volume":"85","author":"C Bert\u00f3k","year":"2016","unstructured":"C. Bert\u00f3k, L. Hajdu, A Hasse-type principle for exponential diophantine equations and its applications. Math. Comput. 85, 849\u2013860 (2016)","journal-title":"Math. Comput."},{"key":"405_CR2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"W. Bosma, J. Cannon, C. Playoust, The Magma algebra system i: the user language. J. Symb. Comput. 24, 235\u2013265 (1997)","journal-title":"J. Symb. Comput."},{"key":"405_CR3","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1023\/A:1015825809661","volume":"132","author":"Y Bugeaud","year":"2002","unstructured":"Y. Bugeaud, Linear forms in two $$m$$-adic logarithms and applications to Diophantine problems. Compos. Math. 132, 137\u2013158 (2002)","journal-title":"Compos. Math."},{"key":"405_CR4","doi-asserted-by":"publisher","first-page":"251","DOI":"10.4064\/aa140-3-3","volume":"140","author":"M Cipu","year":"2009","unstructured":"M. Cipu, M. Mignotte, On a conjecture on exponential Diophantine equations. Acta Arith. 140, 251\u2013269 (2009)","journal-title":"Acta Arith."},{"key":"405_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781316160749","volume-title":"Unit Equations in Diophantine Number Theory","author":"JH Evertse","year":"2015","unstructured":"J.H. Evertse, K. Gy\u0151ry, Unit Equations in Diophantine Number Theory (Cambridge University Press, Cambridge, 2015)"},{"key":"405_CR6","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.jnt.2017.07.004","volume":"183","author":"Y Hu","year":"2018","unstructured":"Y. Hu, M. Le, An upper bound for the number of solutions of ternary purely exponential Diophantine equations. J. Number Theory 183, 62\u201373 (2018)","journal-title":"J. Number Theory"},{"key":"405_CR7","doi-asserted-by":"publisher","first-page":"335","DOI":"10.5486\/PMD.2019.8444","volume":"95","author":"Y Hu","year":"2019","unstructured":"Y. Hu, M. Le, An upper bound for the number of solutions of ternary purely exponential Diophantine equations II. Publ. Math. Debr. 95, 335\u2013354 (2019)","journal-title":"Publ. Math. Debr."},{"key":"405_CR8","first-page":"109","volume":"14","author":"M Le","year":"2019","unstructured":"M. Le, R. Scott, R. Styer, A survey on the ternary purely exponential diophantine equation $$a^x+b^y=c^z$$. Surv. Math. Appl. 14, 109\u2013140 (2019)","journal-title":"Surv. Math. Appl."},{"key":"405_CR9","doi-asserted-by":"publisher","first-page":"373","DOI":"10.4064\/aa153-4-3","volume":"153","author":"F Luca","year":"2012","unstructured":"F. Luca, On the system of Diophantine equations $$a^2+b^2=(m^2+1)^r$$ and $$a^x+b^y=(m^2+1)^z$$. Acta Arith. 153, 373\u2013392 (2012)","journal-title":"Acta Arith."},{"key":"405_CR10","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1216\/RMJ-2015-45-1-303","volume":"45","author":"T Miyazaki","year":"2015","unstructured":"T. Miyazaki, Upper bounds for solutions of an exponential Diophantine equation. Rocky Mountain J. Math. 45, 303\u2013344 (2015)","journal-title":"Rocky Mountain J. Math."},{"key":"405_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4064\/aa8656-2-2018","volume":"186","author":"T Miyazaki","year":"2018","unstructured":"T. Miyazaki, Contributions to some conjectures on a ternary exponential Diophantine equation. Acta Arith. 186, 1\u201336 (2018)","journal-title":"Acta Arith."},{"issue":"1\u20132","key":"405_CR12","doi-asserted-by":"publisher","first-page":"19","DOI":"10.5486\/PMD.2019.8283","volume":"95","author":"T Miyazaki","year":"2019","unstructured":"T. Miyazaki, N. Terai, A study on the exponential Diophantine equation $$a^x+(a+b)^y=b^z$$. Publ. Math. Debr. 95(1\u20132), 19\u201337 (2019)","journal-title":"Publ. Math. Debr."},{"key":"405_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10474-016-0608-z","volume":"149","author":"T Miyazaki","year":"2016","unstructured":"T. Miyazaki, A. Togb\u00e9, P. Yuan, On the Diophantine equation $$a^x + b^y = (a + 2)^z$$. Acta Math. Hungar. 149, 1\u20139 (2016)","journal-title":"Acta Math. Hungar."},{"key":"405_CR14","volume-title":"Catalan\u2019s Conjecture: Are 8 and 9 the Only Consecutive Powers?","author":"P Ribenboim","year":"1994","unstructured":"P. Ribenboim, Catalan\u2019s Conjecture: Are 8 and 9 the Only Consecutive Powers? (Academic Press, Boston, 1994)"},{"key":"405_CR15","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1006\/jnth.1993.1041","volume":"44","author":"R Scott","year":"1993","unstructured":"R. Scott, On the equations $$p^x-b^y=c$$ and $$a^x+b^y=c^z$$. J. Number Theory 44, 153\u2013165 (1993)","journal-title":"J. Number Theory"},{"key":"405_CR16","doi-asserted-by":"publisher","first-page":"131","DOI":"10.5486\/PMD.2016.7282","volume":"88","author":"R Scott","year":"2016","unstructured":"R. Scott, R. Styer, Number of solutions to $$a^x+b^y=c^z$$. Publ. Math. Debr. 88, 131\u2013138 (2016)","journal-title":"Publ. Math. Debr."},{"key":"405_CR17","unstructured":"W. Sierpi\u0144ski, On the equation $$3^x+4^y=5^z$$. Wiadom. Mat. 1, 194\u2013195 (1955\/56) (in Polish)"},{"key":"405_CR18","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1016\/j.jnt.2014.02.009","volume":"141","author":"N Terai","year":"2014","unstructured":"N. Terai, On Je\u015bmanowicz\u2019 conjecture concerning primitive Pythagorean triples. J. Number Theory 141, 316\u2013323 (2014)","journal-title":"J. Number Theory"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-021-00405-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-021-00405-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-021-00405-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T04:41:37Z","timestamp":1652848897000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-021-00405-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,10]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["405"],"URL":"https:\/\/doi.org\/10.1007\/s10998-021-00405-x","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2021,7,10]]},"assertion":[{"value":"3 November 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}