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)

]]

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@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