An easy proof of a 2-prime version of Fermat's little theorem.

If one is in a hurry then this proof allows one to sidestep having to establish all the side work necessary to a proof of the full Euler-Fermat theorem; one merely has to make two applications of the standard Fermat little theorem. We have:

(mod p )

and thus

(mod p )

giving

(mod p )

Similarly

(mod q )

and thus

(mod pq )

since . [End of proof.]

As one quickly learns in RSA public-key cryptography, the 2-prime version of Fermat's 'little' theorem plays a central role.