Problem Set Workbook
Access the downloadable workbook for 2017 USAJMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2017 USAJMO Day 1 math contest by visiting Random Math USAJMO Day 1 2017 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2017 USAJMO Day 1 problems, please refer below:
Problem 1: Prove that there are infinitely many distinct pairs of relatively prime integers and such that is divisible by .
Solution:
Problem 2: Consider the equation
(1) Prove that there are infinitely many pairs of positive integers satisfying the equation.
(2) Describe all pairs of positive integers satisfying the equation.
Solution:
Problem 3: (*) Let be an equilateral triangle and let be a point on its circumcircle. Let lines and intersect at ; let lines and intersect at ; and let lines and intersect at . Prove that the area of triangle is twice the area of triangle .
(c) 2017, Mathematical Association of America.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions