For example, http://www.mathhelpforum.com/math-help/ … ility.html.
]]>Now, Fermats theorem in the language of Galois theory means this:
Putting
gives
If
, we get ; if , the same equation is true as .Ive never seen it stated like this myself so I claim originality for the statement of Fermats little theorem in this form.
]]>I like the combinatorial proof of Fermat's Little Theorem, which considers the number of bracelets that can be made from 'p' beads of 'a' different colours.
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makes it easy to compute the phi function for any integer n, so long as you know its prime factorization.
]]>We have this interesting little result:
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[/align]The proof is only a few lines long. Also:
]]>The proof relies on the multiplicative properties of the sigma function above.
]]>This is something Ive just read about in H.E. Roses A Course in Number Theory. The proof is remarkably simple.
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