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Topic: Euler's theorem? (Read 2631 times) |
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Christine
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Euler's theorem?
« on: Jun 15th, 2013, 1:19pm » |
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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?
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towr
wu::riddles Moderator
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Re: Euler's theorem?
« Reply #1 on: Jun 15th, 2013, 2:03pm » |
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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.
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Wikipedia, Google, Mathworld, Integer sequence DB
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Christine
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Posts: 159
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Re: Euler's theorem?
« Reply #2 on: Jun 15th, 2013, 2:37pm » |
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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?
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