广义商高数的纯指数Diophantine方程a^x+b^y=c^z的解

Solution of Pure Exponential Diophantine Equations a^x+b^y=c^z for Generalized Pythagorean Triplets

运用Gel’fond-Baker方法证明,在m≥105r3时,丢番图方程ax+by=cz仅有正整数解(x,y,z)=(2,2,r).其中r和m为正偶数,(a,b,c)=(|V(m,r)|,|U(m,r)|,m2+1),V(m,r)+U(m,r)(-1)^(1/2)=(m+(-1)^(1/2))r.

Using the Gel＇ fond-Baker method, we prove that if m ≥10^5r3, then the Diophantine equation a^x ＋ b^y = c^z has only one positive integer solution （x,y,z） = （2,2 ,r）. Let r and m be a positive even integer, （a,b,c）=（｜V（m,r）｜,｜U（m,r）｜,m2＋1）,V（m,r）＋U（m,r）√-1=（1/2）=（m＋√-1）r.