关于指数Diophantine方程a^x+b^y=c^z的一个猜想

On a Conjecture Concerning the Exponential Diophantine Equation a^x+b^y=c^z

设r是大干1 的奇数,m是偶数,Ur和Vr是适合 的整数,a=|Vr1,|b=|Ur|,c=m2+1.证明了:当r≡3(mod 4),m≡2(mod 4),m>r/π,且c是素数方幂时,方程az+by=cz仅有正整数解(x,y,z)=(2,2,r).

Let r be an odd integer with r > 1, m be an even integer. Let Ur, Vr beintegers satisfying and c was a power of prime, then the equation ax + by = cz had only the positive integer solution (x,y,z) = (2, 2,r).