On proportionally modular numerical semigroups of embedding dimension three

A numerical semigroup is a submonoid of Z(>= 0) for which its complement in Z(>= 0)is finite. For any set of positive integers a, b, c, the numerical semigroup S(a, b, c) formed by the set of solutions of the inequality ax mod b <= cx is said to be proportionally modular. For any interval [alpha, beta], S([alpha, beta ]) is the submonoid of Z(>= 0 )obtained by intersecting the submonoid of Q(>= 0) generated by [alpha, beta] with Z(>= 0). For the numerical both S(a, b, c) and S([alpha, beta]) equal S. semigroup S of embedding dimension 3, we characterize (a, b, c) and alpha, beta such that