MathDB

B4

Part of 2021 Putnam

Problems(1)

Putnam 2021 B4

Source:

12/5/2021
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.
PutnamPutnam 2021