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0451 combinatorics 4th edition Round 5 p1

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May 7, 2021
combinatorics4th edition

Problem Statement

Let nn be a positive integer and let ana_n be the number of ways to write nn as a sum of positive integers, such that any two summands differ by at least 22. Also, let bnb_n be the number of ways to write nn as a sum of positive integers of the form 5k±15k\pm 1, k∈Zk \in Z. Prove that anbn\frac{a_n}{b_n} is a constant for all positive integers nn.
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