Coins, Stamps, and Quadratic Residues
from 03:00 PM to 04:00 PM
James Joseph Sylvester determined the largest integer number that could not represented as the sum of multiples of two integers a and b whose greatest common divisor was 1. This represents the solution to a problem of Frobenius concerning what would be the largest sum for which a shopkeeper could not make change if coins of denominations a and b are available. It turns out that problems of this kind have an interesting connection to the solution of quadratic congruences. Solving the Frobenius problem with more than two coins available is not totally resolved.