摘要
设n是正整数,(a,b,c)是本原商高数.1956年,L.Jesmanowicz曾经预测:方程(ab)^(x)+(bn)^(y)=(cn)^(z)仅有正整数解(a,b,c)=(2,2,2),这是一个迄今远未解决的数论问题.对于正整数t,设P(t)是t的不同素因数的乘积.运用Baker方法证明了;当n>1,(a,b,c)=(f^(2)-4,4f,f^(2)+4),其中f是适合f>348的奇数时,如果P(n)■a,则Jesmanowicz猜想成立.
Let n be a positive integer,and let(a,b,c) be a primitive Pythagorean triple.In 1956,L.Jesmanowicz’conjectured that the equation(an)^(x)+(bn)^(y)=(cn)^(z) has only the positive integer solution(a,b,c)=(2,2,2),This is a far from solved problem in number theory.For any positive integer t,let P(t) denote the product of distinct prime divisors of t.In this paper,using the Baker method,we prove that if n>1,(a,b,c)=(f^(2)-4,4 f,f^(2)+4) and P(n)+a,where f is an odd integer with f>348,then Jesmanowicz’ conjecture is true.
作者
余亚辉
李振平
YU Ya-hui;LI Zhen-ping(Department of Mathematical Science and Physics,Luoyang Institute of Science and Technology,Luoyang 471023,China)
出处
《数学的实践与认识》
2021年第4期276-281,共6页
Mathematics in Practice and Theory
基金
河南省高等学校青年骨干教师培养计划项目(2019GGJS241)
2020年河南省高等学校重点科研项目计划项目(20A110027)。
