An open problem on Jeśmanowicz′ conjecture concerning primitive Pythagorean triples
Let m>31 be an even integer with gcd(m,31)=1. In this paper, using some elementary methods, we prove that the equation (m2-312)x+(62m)y=(m2+312)z has only the positive integer solution (x,y,z)=(2,2,2). This result resolves an open problem raised by T. Miyazaki (Acta Arith. 186 (2018), 1-36) about...
| Permalink: | http://skupni.nsk.hr/Record/nsk.NSK01001075554/Details |
|---|---|
| Matična publikacija: |
Glasnik matematički (Online) 54 (2019), 2 ; str. 271-277 |
| Glavni autori: | Yang, Hai (Author), Fu, Ruiqin |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.54.2.02 Glasnik matematički (Online) Hrčak |
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| 100 | 1 | |a Yang, Hai |4 aut |9 HR-ZaNSK | |
| 245 | 1 | 3 | |a An open problem on Jeśmanowicz′ conjecture concerning primitive Pythagorean triples |h [Elektronička građa] / |c Hai Yang, Ruiqin Fu. |
| 504 | |a Bibliografija: 7 jed. | ||
| 504 | |a Abstract. | ||
| 520 | |a Let m>31 be an even integer with gcd(m,31)=1. In this paper, using some elementary methods, we prove that the equation (m2-312)x+(62m)y=(m2+312)z has only the positive integer solution (x,y,z)=(2,2,2). This result resolves an open problem raised by T. Miyazaki (Acta Arith. 186 (2018), 1-36) about Jeśmanowicz' conjecture concerning primitive Pythagorean triples. | ||
| 653 | 0 | |a Pitagorine trojke |a Diofantske jednadžbe |a Ternarne operacije | |
| 700 | 1 | |a Fu, Ruiqin |4 aut |9 HR-ZaNSK | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 54 (2019), 2 ; str. 271-277 |w nsk.(HR-ZaNSK)000659858 | |
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