1 Introduction 1.1 The coin exchange problem of Frobenius 1.2 The Frobenius number is well defired 1.3 Amitabha Tripathi's results 1.4 Goal of this paper 2 The two-coin problem 2.1 Tie Frobenius number for two coifs 2.2 Sylvester's Theorem 2.3 More coins 3 More than one representation 3.1 s-representable integers 3.2 Beck-Robins, 20[3 3.3 Brown et al, 2010 3.4 Shailit-Stankewicz, 2010 3.5 Our contribution 3.6 s-representable integers under two coifs 4 Two propositions 5 The Main Theorem 5.1 Tripathi's Theorem 5.2 Extending Tripathi's Theorem 5.3 The Main Theorem Bibliography 編輯手記