       Re: Q in mathematica ??

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• Subject: [mg128999] Re: Q in mathematica ??
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 7 Dec 2012 01:41:53 -0500 (EST)
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On Dec 6, 2012, at 5:01 AM, Q in mathematica <baha791 at gmail.com> wrote:

> Write  Mathematica Blocks that can solve the problem.
>
> Write a code that  verifies   Fermat' s Little Theorem which says that
: If  [Phi](n)  is the Euler Phi  of n, i.e.  the number of positive
integers less than or equal to n which are relatively prime to n,  then
a^[Phi](n)[Congruent]1mod n  for all a  relatively  prime to n.

I hope that wasn't a homework exercise you were asked to do, as it's
straightforward:

Resolve[ForAll[{a, n},
(IntegerQ[a] && IntegerQ[n] && GCD[a, n] == 1)
~Implies~
(Mod[a^EulerPhi[n], n] == 1)
]]
True

Or, the same thing without the quantification:

(IntegerQ[a] && IntegerQ[n] && GCD[a, n] == 1)
~Implies~
(Mod[a^EulerPhi[n], n] == 1)
True

---
Murray Eisenberg                           murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                      413 545-2838 (W)
710 North Pleasant Street                  fax   413 545-1801
Amherst, MA 01003-9305

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