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        riddles >> general problem-solving / chatting / whatever >> Euler's theorem?
        
(Message started by: Christine on Jun 15^th, 2013, 1:19pm)

Title: Euler's theorem?
Post by Christine on Jun 15^th, 2013, 1:19pm

Did Euler prove that:
No sum of three 4-th powers is divisible by either 5 or 29 unless they all are?

I couldn't find it on the web. Can anyone provide a link?

Title: Re: Euler's theorem?
Post by towr on Jun 15^th, 2013, 2:03pm

I can't find a proof by Euler either; but it's pretty much trivial to show it's true (in the worst case just go through all 35 cases mod 5 or the 4495 mod 29, and you can easily do it smarter). I wouldn't expect that Euler would have 'stooped' to publish a proof of it, unless there is a more interesting than trivial way to prove it.

Title: Re: Euler's theorem?
Post by Christine on Jun 15^th, 2013, 2:37pm

Curiously, according to this site

http://www.archimedes-lab.org/numbers/Num24_69.html

'Dictionary of Curious and Interesting Numbers' by David Wells

No sum of three 4th powers is divisible by either 5 or 29 unless they all are. -- Euler

Do you have access to David Wells' book?