【摘要】 设a,b,c是满足条件a2+b2=c2的两两互素的正整数.Jesmanowicz于1956年猜想对于任意给定的正整数n,方程(an)x+(bn)y=(cn)z仅有解(x,y,z)=(2,2,2).本文证明了方程(20n)x+(21n)y=(29n)z有唯一解(x,y,z)=(2,2,2).更多还原

【Abstract】 Let a,b,c be relatively prime positive integers such that a2+b2=c2.A conjecture of Jesmanowicz(1956) is that for any given positive integer n,the only solution of (an)x+(bn)y=(cn)z in positive integers is (x,y,z)=(2,2,2).In this paper,we show that (20n)x+(21n)y=(29n)z has no solution in positive integers other than (x,y,z)=(2,2,2).更多还原