- #1

Ceva

- 12

- 1

It is that one:

## Homework Statement

Find all the integer solutions (x,y) that satisfy the equation:

## Homework Equations

×

^{3}-727× = y

^{3}- 727y

## The Attempt at a Solution

x

^{3}- y

^{3}= 727x - 727y

(x-y)(x

^{2}+xy+y

^{2})=727(x-y)

I didn't divided by (x-y) because i think i'll lose solutions. Also, x-y can be zero (i think).

So i finally have: (x-y)(x

^{2}+xy+y

^{2}-727)=0

How can i continue? Can i factorize more the second bracket? Or i can solve it graphically?

Also, x-y=0 doesn't mean that i have infinite solutions? If i set myself x and y Ε Z .