GENERALIZED FROBENIUS NUMBER OF THREE VARIABLES

For k ≥ 2, we let A = (a 1 , a 2 , . . ., a k ) be a k-tuple of positive integers with gcd(a 1 , a 2 , . . ., a k ) = 1 and, for a non-negative integer s, the generalized Frobenius number of A, g(A; s) = g(a 1 , a 2 , . . ., a k ; s), the largest integer that has at most s representations in terms of a 1 , a 2 , . . ., a k with non-negative integer coefficients.In this paper, we give a formula for the generalized Frobenius number of three positive integers (a 1 , a 2 , a 3 ) with certain conditions.