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Divisibility of Fibonacci sum

Source: ICMC 7 Round 1 Problem 1

January 8, 2024
number theoryFibonacciICMC

Problem Statement

Let FnF_n{} denote the nn{}-th Fibonacci number. Prove that 320233^{2023} divides 32⋅F4+33⋅F6+34⋅F8+⋯+32023F4046.3^2\cdot F_4+3^3\cdot F_6+3^4\cdot F_8+\dots+3^{2023}F_{4046}.Proposed by Dylan Toh
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