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https://doi.org/10.3336/gm.54.2.02

An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples

Hai Yang ; School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi, 710048, P.R. China
Ruiqin Fu ; School of Science, Xi'an Shiyou University, Xi'an, Shaanxi, 710065, P.R. China

Puni tekst: engleski, pdf (104 KB) str. 271-277 preuzimanja: 254* citiraj
APA 6th Edition
Yang, H. i Fu, R. (2019). An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples. Glasnik matematički, 54 (2), 271-277. https://doi.org/10.3336/gm.54.2.02
MLA 8th Edition
Yang, Hai i Ruiqin Fu. "An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples." Glasnik matematički, vol. 54, br. 2, 2019, str. 271-277. https://doi.org/10.3336/gm.54.2.02. Citirano 25.10.2021.
Chicago 17th Edition
Yang, Hai i Ruiqin Fu. "An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples." Glasnik matematički 54, br. 2 (2019): 271-277. https://doi.org/10.3336/gm.54.2.02
Harvard
Yang, H., i Fu, R. (2019). 'An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples', Glasnik matematički, 54(2), str. 271-277. https://doi.org/10.3336/gm.54.2.02
Vancouver
Yang H, Fu R. An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples. Glasnik matematički [Internet]. 2019 [pristupljeno 25.10.2021.];54(2):271-277. https://doi.org/10.3336/gm.54.2.02
IEEE
H. Yang i R. Fu, "An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples", Glasnik matematički, vol.54, br. 2, str. 271-277, 2019. [Online]. https://doi.org/10.3336/gm.54.2.02

Sažetak
Let \(m>31\) be an even integer with \(\gcd(m,31)=1\). In this paper, using some elementary methods, we prove that the equation \((m^2-31^2)^x+(62m)^y=(m^2+31^2)^z\) has only the positive integer solution \((x,y,z)=(2,2,2)\). This result resolves an open problem raised by T. Miyazaki ({\em Acta Arith.} 186 (2018), 1--36) about Je\'smanowicz' conjecture concerning primitive Pythagorean triples.

Ključne riječi
Ternary purely exponential Diophantine equation; Jeśmanowicz' conjecture; primitive Pythagorean triple; elementary method

Hrčak ID: 229599

URI
https://hrcak.srce.hr/229599

Posjeta: 416 *