擴展線性丟番圖問題（英文）

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
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