This'll be my first question in the Mathematics section, I've stumbled upon here quite a lot, so here I stand before you today to ask a question myself...
There's this question which I've been unable to solve for years. It's from some nationwide competition held in Turkey.
The question asks the following:
(20!*12!) mod 2012 is equivalent to which of the following? A) 344 B) 1062 C) 736 D) 162 E) None of the Above
The answer is:
Do note that:
A valid answer would be 1684
Now sure, I could just plug this into a calculator and find the answer... But how were the poor kids who took this exam meant to solve it?
Through several reductions I myself was, and several other people I've asked the question were, able to reduce the problem to the following:
4*[ 60 * 11! * 19! mod 503 ]
Now that still looks terribly ugly, what I've really been searching for is an easy way to calculate
11! mod 503 and
19! mod 503. Is there any theorem or the such which will allow me to easily calculate
the Remainder of a Prime Factorial Divided by a Prime Number. (And yes, I can assure you that 11, 19 and 503 are all prime numbers.) Any help would be much appreciated, thank you all in advance...