A note on Terai's conjecture concerning primitive Pythagorean triples
Yıl: 2021 Cilt: 50 Sayı: 4 Sayfa Aralığı: 911 - 917 Metin Dili: İngilizce DOI: 10.15672/hujms.795889 İndeks Tarihi: 29-07-2022
A note on Terai's conjecture concerning primitive Pythagorean triples
Öz: Let $f,g$ be positive integers such that $f>g$, $gcd(f,g)=1$ and $fnotequiv g pmod{2}$. In 1993, N. Terai conjectured that the equation $x^2+(f^2-g^2)^y=(f^2+g^2)^z$ has only one positive integer solution $(x,y,z)=(2fg,2,2)$. This is a problem that has not been solved yet. In this paper, using elementary number theory methods with some known results on higher Diophantine equations, we prove that if $f=2^rs$ and $g=1$, where $r,s$ are positive integers satisfying $2nmid s$, $rge 2$ and $s<2^{r-1}$, then Terai's conjecture is true.
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| APA | Le M, soydan g (2021). A note on Terai's conjecture concerning primitive Pythagorean triples. , 911 - 917. 10.15672/hujms.795889 |
| Chicago | Le Maohua,soydan gokhan A note on Terai's conjecture concerning primitive Pythagorean triples. (2021): 911 - 917. 10.15672/hujms.795889 |
| MLA | Le Maohua,soydan gokhan A note on Terai's conjecture concerning primitive Pythagorean triples. , 2021, ss.911 - 917. 10.15672/hujms.795889 |
| AMA | Le M,soydan g A note on Terai's conjecture concerning primitive Pythagorean triples. . 2021; 911 - 917. 10.15672/hujms.795889 |
| Vancouver | Le M,soydan g A note on Terai's conjecture concerning primitive Pythagorean triples. . 2021; 911 - 917. 10.15672/hujms.795889 |
| IEEE | Le M,soydan g "A note on Terai's conjecture concerning primitive Pythagorean triples." , ss.911 - 917, 2021. 10.15672/hujms.795889 |
| ISNAD | Le, Maohua - soydan, gokhan. "A note on Terai's conjecture concerning primitive Pythagorean triples". (2021), 911-917. https://doi.org/10.15672/hujms.795889 |
| APA | Le M, soydan g (2021). A note on Terai's conjecture concerning primitive Pythagorean triples. Hacettepe Journal of Mathematics and Statistics, 50(4), 911 - 917. 10.15672/hujms.795889 |
| Chicago | Le Maohua,soydan gokhan A note on Terai's conjecture concerning primitive Pythagorean triples. Hacettepe Journal of Mathematics and Statistics 50, no.4 (2021): 911 - 917. 10.15672/hujms.795889 |
| MLA | Le Maohua,soydan gokhan A note on Terai's conjecture concerning primitive Pythagorean triples. Hacettepe Journal of Mathematics and Statistics, vol.50, no.4, 2021, ss.911 - 917. 10.15672/hujms.795889 |
| AMA | Le M,soydan g A note on Terai's conjecture concerning primitive Pythagorean triples. Hacettepe Journal of Mathematics and Statistics. 2021; 50(4): 911 - 917. 10.15672/hujms.795889 |
| Vancouver | Le M,soydan g A note on Terai's conjecture concerning primitive Pythagorean triples. Hacettepe Journal of Mathematics and Statistics. 2021; 50(4): 911 - 917. 10.15672/hujms.795889 |
| IEEE | Le M,soydan g "A note on Terai's conjecture concerning primitive Pythagorean triples." Hacettepe Journal of Mathematics and Statistics, 50, ss.911 - 917, 2021. 10.15672/hujms.795889 |
| ISNAD | Le, Maohua - soydan, gokhan. "A note on Terai's conjecture concerning primitive Pythagorean triples". Hacettepe Journal of Mathematics and Statistics 50/4 (2021), 911-917. https://doi.org/10.15672/hujms.795889 |
