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Largest postage impossible with 5 and 21 stamps

Question

You have unlimited stamps worth 55 and 2121. What is the largest total value you cannot make exactly?

Short answer

79. For coprime a,ba,b the largest non-representable value is ab−a−bab-a-b (Frobenius), here 105−26=79105-26=79. Concretely, the cheapest way to reach residue 4(mod5)4\pmod5 is 84=4⋅2184=4\cdot21, so 7979 is the largest value in that class that is unreachable.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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