Euler's Conjecture 

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Euler's conjecture is closely related to Fermat's Last theorem. Fermat's Last Theorem states that, although there are tripples such as a, b, c for which it is true to say there are no numbers x, y, and z for which is valid, when n>2. Euler, in 1769 proposed that there are no sets of numbers such that or OR, in general terms, there are any sets of n1 numbers such that the sum of their nth power would also be an nth power. The conjecture was disproved in 1966 by Lander and Parkin who found counterexample for n=5: Another counterexample was found by Noam Elkies in 1988: Another counterexample was given by Roger Frye who found the smallest possible n=4 solution
Something for you to do: First write down Euler's conjecture in algebraic notation. Try combinations for n>5. No known solutions are found so far!

See more about Euler by cliking on his picture above. See what the difference is between a conjecture and a theorem. Fermat's Last Theorem  click on the equation. You can download a presentation on Fermat's Last Theorem by clicking on the picture below.


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