## Euler's conjectureEuler'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 27^{5} + 84^{5} + 110^{5} + 133^{5} = 144^{5}.
In 1988 Noam Elkies of Harvard University found a counterexample for fourth
powers: 2,682,440^{4} + 15,365,639^{4} + 187,960^{4} = 20,615,673^{4}. Subsequently, Roger Frye of Thinking Machines
Corporation did a computer search to find the smallest example: 95,800^{4} + 217,519^{4} + 414,560^{4} = 422,481^{4}. ## Related category• NUMBER THEORY | |||||

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