Solutions 2

Level pending

Which of these x's do not constitute to a part of an integer solution to x+x^2=y+y^3

-6 -2 2 -1 1 0

1 solution

Vinayak Srivastava
May 20, 2020

For $x=0$ , $y+y^3=0 \implies y=0$ .

For $x=1$ , $y+y^3=2 \implies y=1$ .

For $x=-1$ , $y+y^3=0 \implies y=0$ .

For $x=-2$ , $y+y^3=2 \implies y=1$ .

For $x=-6$ , $y+y^3=30 \implies y=3$ .

But for $x=2$ , $y+y^3=10$ , which has no integer solution for $y$ .

Hence the answer is $\boxed{2}$