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Putnam 2020 A5

Source: 81st William Lowell Putnam Competition

February 22, 2021
PutnamPutnam 2020

Problem Statement

Let ana_n be the number of sets SS of positive integers for which ∑k∈SFk=n, \sum_{k\in S}F_k=n, where the Fibonacci sequence (Fk)k≥1(F_k)_{k\ge 1} satisfies Fk+2=Fk+1+FkF_{k+2}=F_{k+1}+F_k and begins F1=1F_1=1, F2=1F_2=1, F3=2F_3=2, F4=3F_4=3. Find the largest number nn such that an=2020a_n=2020.
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