MathDB
Putnam 2021 B4

Source:

December 5, 2021
PutnamPutnam 2021

Problem Statement

Let F0,F1,…F_0,F_1,\dots be the sequence of Fibonacci numbers, with F0=0,F1=1F_0=0,F_1=1, and Fn=Fn−1+Fn−2F_n=F_{n-1}+F_{n-2} for n≥2n \ge 2. For m>2m>2, let RmR_m be the remainder when the product ∏k=1Fm−1kk\prod_{k=1}^{F_m-1} k^k is divided by FmF_m. Prove that RmR_m is also a Fibonacci number.
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