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--- pow:problem4f22 [2022/10/29 01:39] – mazur
+++ pow:problem4f22 [2022/10/29 01:40] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| Problem 4 (due on Monday, October 24)>
+A sequence $(a_n)$ of positive integers has been created using the following process:
+\[ a_{n+1}=a_n+3\frac{a_n}{p_n}\]
+where $p_n$ is a prime divisor of $a_n$. Prove that there is a positive integer $k$ such that the equality
+$a_{n+k}=2ka_n$ holds for infinitely many values of $n$.
+</box>
+We received a solution from Garrett Gramzow, Prof. Vladislav Kargin, and Ashton Keith. All three
+solutions as well as our original solution are essentially following the same line of argument,
+though Garrett's solution needs some improvements in exposition. It turns out that
+either $k=1$ or $k=2$ works. For a detailed solution see the following link {{:pow:2022fproblem4.pdf|Solution}}.