Just finished reading neat and combinatorial proofs of "Fermat's Little Theorem" and "Wilson's Theorem" (although only in one direction) in George E. Andrews's "Number Theory" book from Dover.

While this seems to be an elementary book on Number Theory (it
covers just the basics---which I have been trying to learn for some
time now) it is also *quite* well-written. Perhaps some writers of
computer books could learn a thing or two with Mathematicians.