# Research done by high-school students

I’m giving a talk soon to a group of high-school students about open problems in mathematics that high-school students could understand. To inspire them, I would like to give them examples of high-school students who have made original contributions in mathematics. One example I have is the 11th-grader from Hawai’i named Kang Ying Liu who in 2010 “discover[ed] nine new geometric formulas for describing triangle inequalities.”

Do you have any other examples of high-school students who have made original contributions in mathematics?

Let $a$ and $b$ be positive integers such that $ab+1$ divides $a^2+b^2$. Prove $\frac{a^2+b^2}{ab+1}$ is a perfect square.