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    OlympiadMediumNumber Theory5–6

    Frobenius Theorem

    Teorema de Frobenius

    What is the largest amount of money that cannot be obtained using only 3-cent and 5-cent coins?

    List the amounts you can actually form with 3s and 5s, in order, and look for the point where the gaps stop.

    Solution

    Step 1 of 6

    1. 1.Amounts that can be formed: 3,5,6,8,9,10,11,12,13,14,15,…3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, \ldots