On the Frobenius Problem

Abstract: The classical Frobenius problem (the Frobenius coin problem) is considered. Using themethod of generating functions, we find an expression for the number of solutions of a Diophantineequation. As a corollary, this result implies the well-known Sylvester–Gallai theorem. In addition,we obtain not only an expression for the Frobenius number, but also formulas for those values ofthe variables for which this number is attained. The problems in this paper are closely related todiscrete optimization problems as well as cryptographic information security methods. © 2022, Pleiades Publishing, Ltd.