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solve a equation with fibonacci coefficients

Source: Mathematics Regional Olympiad of Mexico Southeast 2023 P4

October 8, 2023
algebraFibonacci

Problem Statement

Given the Fibonacci sequence with f0=f1=1f_0=f_1=1and for n≥1,fn+1=fn+fn−1n\geq 1, f_{n+1}=f_n+f_{n-1}, find all real solutions to the equation: x2024=f2023x+f2022.x^{2024}=f_{2023}x+f_{2022}.
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