Jeśmanowicz猜想的一类特殊情形

Special Case of Jeśmanowicz’Conjecture

设(a,b,c)为本原Pythagorean三元数组,n为正整数,P(a)表示a的所有不同素因子的乘积,本文证明了当a≡-1(modb),P(a)|n时,指数丢番图方程(an)x+(bn)y=(cn)z只有正整数解(2,2,2)。

Let n be a positive integer,and let(a,b,c)be a primitive Pythagorean triple.Denote by P(a)the product of distinct prime divisors of a.In this paper,we prove that if a≡-1(modb)and P(a)|n,then the Diophantine equation(an)x+(bn)y=(cn)z has no solution other than(2,2,2)in positive integers.