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 n-1 numbers such that the sum of their n-th power would also be an n-th 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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