Question 76
Let $n \in \mathbb{N}^*$ and $(G, \cdot)$ be a group with the property that there exists an endomorphism $f : G \to G$, so that
$$
f(x^n y^{n+1}) = x^{n+1} y^n \text{ for every } x, y \in G
$$
$$
f(x^n y^{n+1}) = x^{n+1} y^n \text{ for every } x, y \in G
$$