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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 5491020 (H) University of Massachusetts 413 5452838 (W) 710 North Pleasant Street fax 413 5451801 Amherst, MA 010039305



