Problem Set Workbook
Access the downloadable workbook for 2018 USAMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2018 USAMO Day 1 math contest by visiting Random Math USAMO Day 1 2018 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2018 USAMO Day 1 problems, please refer below:
Problem 1: Let be positive real numbers such that . Prove that
Solution:
Problem 2: Find all functions such that
for all with .
Solution:
Problem 3: For a given integer , let be the set of positive integers less than that are relatively prime to . Prove that if every prime that divides also divides , then is divisible by for every positive integer .
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions