A note on the exponential Diophantine equation (A 2n) x+(B 2n) y=((A 2+B 2)n) z
Let A, B be positive integers such that min{A,B}>1, gcd(A,B) = 1 and 2|B. In this paper, using an upper bound for solutions of ternary purely exponential Diophantine equations due to R. Scott and R. Styer, we prove that, for any positive integer n, if A >B3/8, then the equation (A2 n)x + (B2 n...
| Permalink: | http://skupni.nsk.hr/Record/nsk.NSK01001098337/Details |
|---|---|
| Matična publikacija: |
Glasnik matematički (Online) 55 (2020), 2 ; str. 195-201 |
| Glavni autori: | Le, Maohua (Author), Soydan, Gökhan |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.55.2.03 Hrčak |
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| 008 | 210420s2020 ci |o |0|| ||eng | ||
| 024 | 7 | |2 doi |a 10.3336/gm.55.2.03 | |
| 035 | |a (HR-ZaNSK)001098337 | ||
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| 041 | 0 | |a eng |b eng | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Le, Maohua |4 aut | |
| 245 | 1 | 2 | |a A note on the exponential Diophantine equation (A 2n) x+(B 2n) y=((A 2+B 2)n) z |h [Elektronička građa] / |c Maohua Le, Gökhan Soydan. |
| 504 | |a Bibliografske bilješke na kraju teksta. | ||
| 504 | |a Abstract. | ||
| 520 | |a Let A, B be positive integers such that min{A,B}>1, gcd(A,B) = 1 and 2|B. In this paper, using an upper bound for solutions of ternary purely exponential Diophantine equations due to R. Scott and R. Styer, we prove that, for any positive integer n, if A >B3/8, then the equation (A2 n)x + (B2 n)y = ((A2 + B2)n)z has no positive integer solutions (x,y,z) with x >z >y; if B>A3/6, then it has no solutions (x,y,z) with y>z>x. Thus, combining the above conclusion with some existing results, we can deduce that, for any positive integer n, if B ≡ 2 (mod 4) and A >B3/8, then this equation has only the positive integer solution (x,y,z)=(1,1,1). | ||
| 653 | 0 | |a Diofantske jednadžbe |a Eksponencijalne jednadžbe | |
| 700 | 1 | |a Soydan, Gökhan |4 aut |9 HR-ZaNSK | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 55 (2020), 2 ; str. 195-201 |w nsk.(HR-ZaNSK)000659858 | |
| 981 | |b Be2020 |b B03/20 | ||
| 998 | |b tino2106 | ||
| 856 | 4 | 0 | |u https://doi.org/10.3336/gm.55.2.03 |
| 856 | 4 | 0 | |u https://hrcak.srce.hr/248663 |y Hrčak |
| 856 | 4 | 1 | |y Digitalna.nsk.hr |