2024 USAJMO Problems
Contents
[hide]Day 1
Problem 1
Let be a cyclic quadrilateral with and . Points and are selected on line segment so that . Points and are selected on line segment so that . Prove that is a quadrilateral.
Problem 2
Let and be positive integers. Let be the set of integer points with and . A configuration of rectangles is called happy if each point in is a vertex of exactly one rectangle, and all rectangles have sides parallel to the coordinate axes. Prove that the number of happy configurations is odd.
Problem 3
Let be the sequence defined by and for each integer . Suppose that is prime and is a positive integer. Prove that some term of the sequence is divisible by .