How to solve in integers the equation $y^k=x^2+x$

Question

How to solve in integers the equation $$y^k=x^2+x$$ where $k\ge 2, k \in \mathbb N$.

My work so far

1) $x^2+x=x(x+1)$. But $\gcd(x,x+1)=1$

Then $$y\cdot y\cdot...\cdot y=x(x+1)$$

2) If $k=2n$. Then $$y^k=x(x+1)$$ $$\left(y^n\right)^2=x(x+1)$$ Then $x=m^2, x+1=l^2$. Impossible

3) If $n=2k+1$.

I need help here

Answer 1

Hint: both $x$ and $x+1$ must be $k$'th powers.