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--- pow:problem4f23 [2023/10/22 00:13] – created mazur
+++ pow:problem4f23 [2023/11/02 17:07] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| 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 $n$.
+</box>
+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 {{:pow:2023fproblem4.pdf|Solution}}.