```Date: Dec 7, 2012 1:38 AM
Author: Murray Eisenberg
Subject: Re: Q in mathematica ??

On Dec 6, 2012, at 5:01 AM, Q in mathematica <baha791@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)          ]] TrueOr, 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@math.umass.eduMathematics & Statistics Dept.      Lederle Graduate Research Tower            phone 413 549-1020 (H)University of Massachusetts                      413 545-2838 (W)710 North Pleasant Street                  fax   413 545-1801Amherst, MA 01003-9305
```