Perfect powers as sum of consecutive powers

In 1770 Euler observed that $3^3 + 4^3 + 5^3 = 6^3$ and asked if there was another perfect power that equals the sum of consecutive cubes. This captivated the attention of many important mathematicians, such as Cunningham, Catalan, Genocchi and Lucas. In the last decade, the more general equation $x^k + (x+1)^k + \cdots + (x+d)^k = y^n$ began to be studied. In this talk we will focus on this equation. We will see some known results and one of the most used tools to attack this kind of problems. At the end we will show some new results that appear in arXiv:2404.03457.