Art of Problem Solving

AoPS Online

2024 USAJMO Problems/Problem 3

Revision as of 21:43, 19 March 2024 by Ryanjwang (talk | contribs) (Created page with "=== Problem === Let <math>a(n)</math> be the sequence defined by <math>a(1)=2</math> and <math>a(n+1)=(a(n))^{n+1}-1</math> for each integer <math>n\geq1</math>. Suppose that...")

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $a(n)$ be the sequence defined by $a(1)=2$ and $a(n+1)=(a(n))^{n+1}-1$ for each integer $n\geq1$ . Suppose that $p>2$ is prime and $k$ is a positive integer. Prove that some term of the sequence $a(n)$ is divisible by $p^k$ .

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2024_USAJMO_Problems/Problem_3&oldid=217145"

© 2024 AoPS Incorporated