# Problem of the Month

• Everyone is welcome to participate, but only undergraduate OU students are eligible for the prizes.
• At the end of the academic year, a prize will be awarded to the undergraduate OU students with the most correct solutions.
• A complete solution to the problem must include a proof.
• Solutions to the Problem of the Month can be submitted in the Math Department's office (PHSC 423), or via email to nickmbmiller [at] ou [dot] edu
• Make sure that your submission includes your name and OU email.
• The deadline for submission is the last day of the month.
• The problem of the month during the summer months of May, June, July, and August will not be graded and are just for fun.

Winners of the academic year 2022/23 are Matthew Hudson and Jacob Norris.

## Thurston's Pentagon

Suppose that each vertex of a pentagon is given an integer in such a way that the sum of the five numbers is positive. Given three consecutive vertices with integers a, b, c for which b<0, an allowable move is one where you replace a, b, c by a+b, -b, b+c (respectively). Is there always a finite sequence of allowable moves which makes all five integers positive? Prove it or give a counterexample.