# 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.

### December 2022

## Subsets of the reals

Let S={x_{1},...,x_{N}} be an arbitrary set of N distinct real numbers. How large must N, the number of elements of S, be to guarantee that there are two elements x,y of S which satisfy the inequalities 0<(x-y)/(1+xy)<2-√3?