TY  - JOUR
TI  - A note on Terai's conjecture concerning primitive Pythagorean triples
AB  - 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.
AU  - soydan, gokhan
AU  - Le, Maohua
DO  - 10.15672/hujms.795889
PY  - 2021
JO  - Hacettepe Journal of Mathematics and Statistics
VL  - 50
IS  - 4
SN  - 1303-5010
SP  - 911
EP  - 917
DB  - TRDizin
UR  - http://search/yayin/detay/493988
ER  -