A note on Je?manowicz’ conjecture |
| |
Authors: | Q Han P Yuan |
| |
Institution: | 1.Faculty of Common Courses,South China Business College of Guangdong University of Foreign Studies,Guangzhou,China;2.School of Mathematics,South China Normal University,Guangzhou,China |
| |
Abstract: | Je?manowicz 9] conjectured that, for positive integers m and n with m > n, gcd(m,n) = 1 and \({m\not\equiv n\pmod{2}}\), the exponential Diophantine equation \({(m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z}\) has only the positive integer solution (x, y, z) = (2, 2, 2). We prove the conjecture for \({2 \| mn}\) and m + n has a prime factor p with \({p\not\equiv1\pmod{16}}\). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|