For anyone fascinated by powers and integers, there’s no shortage of problems to tackle, whether by ingenious logic or massive computer search.
In 1769, while thinking about the problem now known as Fermat’s last theorem, Leonhard Euler (1707–1783) proposed an intriguing variant.
A century earlier, Pierre de Fermat (1601–1665) had proved that no set of positive integers, a, b, and c, satisfies the equation a4 + b4 = c4 in the same way that numbers such as 3, 4, and 5 satisfy the more familiar equation x2 + y2 = z2. Euler conjectured that the equation a4 + b4 + c4 = d4 would also have no integer solutions.