关于Diophantine方程x^(p-1)-1=2~mpy^n

ON THE DIOPHANTINE EQUATION x^(p-1)-1=2~mpy^n

设p是奇素数 ,n是大于 1的奇数 .证明了 :当p≡7(mod 12 )时 ,方程xp -1- 1=2 mpyn 无正整数解 (x ,y,m ,n) .

Let p be an odd prime,and let n be an odd integer with n>1 .that if p≡7 (mod 12),then the equation x p-1 -1=2 mpy n had no positive integer solutions (x,y,m,n) was proven.