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Topic: Q in mathematica ??
Replies: 2   Last Post: Dec 8, 2012 1:28 AM

 Messages: [ Previous | Next ]
 Murray Eisenberg Posts: 2,105 Registered: 12/6/04
Re: Q in mathematica ??
Posted: Dec 7, 2012 1:38 AM

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

Date Subject Author
12/7/12 Murray Eisenberg
12/8/12 Richard Fateman