Re: Mod 2011


"Jyrki Lahtonen" <lahtonen@xxxxxx> wrote in message
news:eoihr0$1ac0$2@xxxxxxxxxxxxxxxxx
León-Sotelo wrote:
Determine the remainder when 1004! is divided by 2011.

Thanks
León-Sotelo


Check whether 2011 is a prime or not. If it isn't, the
answer is easy to deduce. If it is (as I suspect), then
one has to resort to Wilson's theorem (and basic facts about
finite fields). Hint: 1004 is very close to half of 2010.

For the unitiated Wilson's Theorem apparently states:

Iff p is a prime, then (p-1)! is a multiple of p , that is (p-1)! is
equivalent to -1 (mod p)

http://mathworld.wolfram.com/WilsonsTheorem.html

Nick


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