# Problem of the Month

- Everyone is welcome to participate, but only undergraduate OU students are eligible for the prizes.
- If there is more than one correct submission, the evaluation committee will select a winner.
- 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 jachavezd [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.

### February 2022

## Questionable gift choices

As a Valentine's day gift, a quirky student has requested from their beloved a set of positive integers. For obvious aesthetic reasons the set should consist of consecutive numbers, and it should contain as many multiples of 3 as it contains multiples of 5.

What is the largest possible size of a set satisfying these conditions?