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### How many ways are there to exchange n pennies using two(or more) types of coins?

**Algebra & Discrete Mathematics**

Speaker: | Prof. Sinai Robins, Temple University |

Location: | 593 Kerr |

Start time: | Thu, May 2 2002, 4:10PM |

The coin exchange problem asks for the number of ways we can exchange n pennies by using finitely many coins. That is, we're given a positive integer n and positive integers a_i (the coins) whose gcd is 1. We then ask for positive integers x_j that solve the linear relation n = a_1 x_1 + ... + a_d x_d. This problem brings together many fields, and in the course of studying this problem we uncover some interesting new connections between combinatorics, analytic number theory (Dedekind sums), and convex polytopes.

Today is a two-speaker session (Lipika Deka speaks at 15:10pm).