Problem 4 (due Monday, October 23)
Let $f(x)=ax^2+bx+c$ be a quadratic polynomial with integral coefficients. Suppose that there are $n\geq 5$ consecutive integers at which the value of $f$ is a perfect square. Prove that $b^2-4ac$ is divisible by every prime number smaller or equal than $n$.
The problem was solved by Dr. Mathew Wolak. Matt's solution is essentially the same as one of our in-house solutions. For detailed solutions, some additional discussion and related open questions see the following link Solution.