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.

Summer cubics

Let p(x)=x³+17. For every integer n≥2, show that there exists a natural number x for which p(x) is divisible by 3ⁿ but not by 3ⁿ⁺¹.