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 2023/24 is Jacob Norris.

July 2024

Polynomial values

Let P(x)=a_nxⁿ+a_n-1x^n-1+...+a₀ be a polynomial of degree n with real coefficients and let r be any real number greater than or equal to 3. Show that there exists some j between 0 and n for which |P(j)-r^j| is at least 1.