不定方程■的正整数解

Positive Integer Solution on the Indeterminate Equation ■

设k,l,m_(1),m_(2)是正整数,p,q为奇素数且满足pk=2m1-3m2,q^(l)=2^(m1)+3^(m2).证明了若2■m_(1),m_(2)≡2(mod 4),z≡0(mod 2),则对任意正整数n>1,丢番图方程■仅有正整数解(x,y,z)=(2,2,2),从而得到Jesmanowicz猜想在该情形下的正确性.

Let k,l,m_(1),m_(2) be positive integers,and p,q be odd primes,so that pk=2^(m1)-3^(m2),q^(1)=2^(m1)+3^(m2).It is proved that if 2■m_(1),m_(2)■_(2)(mod 4),z■0(mod 2),for any positive integer”〉1,the Diophantine equation■has only positive integer solution(x,y,z)=(2,2,2),which confirms the Jesmanowicz conjecture in this case.