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- W1939557908 abstract "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 0le rle M-1 then CH(n) restricted to n equiv r mod M is a poly, (2) If 0le rle M'-1 then CH(n) restricted to nequiv 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." @default.
- W1939557908 created "2016-06-24" @default.
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- W1939557908 date "2015-07-16" @default.
- W1939557908 modified "2023-09-22" @default.
- W1939557908 title "Three Results on Making Change (An Exposition)" @default.
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