WEIGHTED SYLVESTER SUMS ON THE FROBENIUS SET IN MORE VARIABLES

Abstract

Given positive integers a1, . . . , ak with gcd(a1, . . . , ak) = 1, it is well-known that all sufficiently large n can be represented as a nonnegative integer combination of a1, . . . , ak. The Frobenius Problem is to determine the largest positive integer that is NOT representable as a nonnegative integer combination of given positive integers that are coprime (see [15] for general references). This number is denoted by g(a1, . . . , ak) and often called Frobenius number. The Frobenius Problem has been also known as the Coin Exchange Problem (or Postage Stamp Problem / Chicken McNugget Problem), which