  Assume you an infinite supply of pennies, nickels, dimes, and quarters (or
some other finite set of denominations which are relatively prime). Let CH(n)
be the number of ways to make change of n cents. We present a simple unified
exposition of three know theorems about CH(n). Let M be the LCM of a1,...,aL.
Let M' be the LCM of the GCD of all pairs of ai's. (1) If 0\le r\le M-1 then
CH(n) restricted to n \equiv r mod M is a poly, (2) If 0\le r\le M'-1 then
CH(n) restricted to n\equiv r mod M' is a poly except for the constant term,
(3) CH(n) is n^{L-1}/(L-1)!a1a2...aL + O(n^{L-2}). Part (3) is known as Schur's
theorem.
