Find all ordered pairs of nonnegative integers $(x,y)$ such that \[x^4-x^2y^2+y^4+2x^3y-2xy^3=1.\]
Problem
Source: Moldova 2017 TST, B11
Tags: number theory
Snakes
21.03.2017 01:00
Wave-Particle wrote:
Note that $x^4-x^2y^2+y^4+2x^3y-2xy^3=(x^2+xy-y^2)^2$.
The solution is not as easy as you think
Wave-Particle
21.03.2017 01:08
Snakes wrote: Wave-Particle wrote:
Note that $x^4-x^2y^2+y^4+2x^3y-2xy^3=(x^2+xy-y^2)^2$.
The solution is not as easy as you think Write it as a Pell Equation $(2x+y)^2-5y^2=4$
test20
21.03.2017 12:45
This is essentially equivalent to problem 3 of IMO 1981: https://artofproblemsolving.com/community/c6h60816p366642