Euler's conjecture is that it always takes n terms to sum to an n-th power: two squares, three cubes, four fourth powers, and so. This hypothesis is now known to be wrong. In 1966, L. J. Lander and T. R. Parkin found the first counterexample: four fifth powers that sum to a fifth power. They showed that 275 + 845 + 1105 + 1335 = 1445. In 1988 Noam Elkies of Harvard University found a counterexample for fourth powers: 2,682,4404 + 15,365,6394 + 187,9604 = 20,615,6734. Subsequently, Roger Frye of Thinking Machines Corporation did a computer search to find the smallest example: 95,8004 + 217,5194 + 414,5604 = 422,4814.
Related category NUMBER THEORY
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