Encyclopedia > Euler's conjecture

  Article Content

Euler's conjecture

Euler's conjecture is a conjecture related to Fermat's Last Theorem which was proposed by Leonhard Euler in 1769. It states that for every integer n greater than 2, the sum of n-1 n-th powers of positive integers cannot itself be an n-th power.

The conjecture was disproved by L. J. Lander[?] and T. R. Parkin[?] in 1966 when they found the following counterexample for n = 5:

275 + 845 + 1105 + 1335 = 1445.

In 1988, Noam Elkies[?] found a method to construct counterexamples for the n = 4 case. His smallest counterexample was the following:

26824404 + 153656394 + 187967604 = 206156734.

Roger Frye[?] subsequently found the smallest possible n = 4 counterexample by a direct computer search using techniques suggested by Elkies:

958004 + 2175194 + 4145604 = 4224814.

No counterexamples for n > 5 are currently known.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Mayenne

...     Contents Mayenne Mayenne is a French département, number 53, named after the Mayenne River[?]. Préfecture (capital): ...

 
 
 
This page was created in 35.8 ms