Problem of the Week

Problem 7 (due Monday, December 4)

Find the smallest positive integer which cannot be expressed as a sum of 2023 or fewer Fibonacci numbers (not necessarily distinct). Recall that the Fibonacci numbers $f_n$ are defined recursively as follows: $f_1=f_2=1$, $f_{n}=f_{n-1}+f_{n-2}$ for all $n>2$.

Overview

Every other Monday (starting 08/28/23), we will post a problem to engage our mathematical community in the problem solving activity and to enjoy mathematics outside of the classroom. Students (both undergraduate and graduate) are particularly encouraged to participate as there is no better way to practice math than working on challenging problems. If you have a solution and want to be a part of it, e-mail your solution to Marcin Mazur (mazur@math.binghamton.edu) by the due date. We will post our solutions as well as novel solutions from the participants and record the names of those who've got the most number of solutions throughout each semester.

When you submit your solutions, please provide a detailed reasoning rather than just an answer. Also, please include some short info about yourself for our records.

Previous Problems and Solutions

Problem 6 No correct solutions were received.

Problem 5 Solved by Sasha Aksenchuk, Dr. Saurabh A. Chandorkar (Indian Institute of Science), Prof. Vladislav Kargin, Mithun Padinhare Veettil, Eric Wang.