## The Positive Integer Solutions of Equation Ax^m+By^n=Cz^k

**Authors:** Haofeng Zhang

In this paper for equation Ax^m+By^n=Cz^k , where m,n,k > 2, x,y,z > 1, A,B,C≥1 and gcd(Ax,By,Cz)=1, the author proved there are no positive integer solutions for this equation using“Order reducing method for equations” that the author invented for solving high order equations,in which let the equation become two equations, through comparing the two roots to prove there are no positive integer solutions for this equation.

**Comments:** 30 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-01-17 06:15:54

[v2] 2018-01-28 11:08:53

**Unique-IP document downloads:** 23 times

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