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

**Authors:** Haofeng Zhang

In this paper for equation Axm+Byn=Czk , where m,n,k > 2, x,y,z > 2, A,B,C≥1 and gcd(Ax,By,Cz)=1, the author proves 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 under the assumption of no positive integer solutions for Ax^3+By^3=Cz^3 when Ax^m-i+By^n-i>Cz^k-i.

**Comments:** 30 Pages.

**Download:** **PDF**

### Submission history

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

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

[v3] 2018-03-09 05:47:15

[v4] 2018-03-17 12:52:43

**Unique-IP document downloads:** 52 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*