Puzzles
Euler guessed you need 5 fifth-powers to sum to another fifth power. Was he right?
In 1769, Leonhard Euler conjectured that you need at least n whole numbers, each raised to the nth power, to add up to another perfect nth power — an extension of Fermat's Last Theorem. Could anyone ever find a counterexample?
Reveal the answer
Yes — nearly 200 years later. In 1966, mathematicians L.J. Lander and T.R. Parkin ran a computer search and found 27⁵ + 84⁵ + 110⁵ + 133⁵ = 144⁵, just four fifth-powers summing to a fifth power, disproving Euler's conjecture. Their published paper was just two sentences long, one of the shortest research papers ever written.