Individual Problems and Solutions
For problems and detailed solutions to each of the 2002 USAMO problems, please refer below:
Problem 4: Let be the set of real numbers. Determine all functions such that
for all real numbers and .
Solution:
Problem 5: Let be integers greater than 2. Prove that there exists a positive integer and a finite sequence of positive integers such that , and is divisible by for each .
Solution:
Problem 6: I have an sheet of stamps, from which I've been asked to tear out blocks of three adjacent stamps in a single row or column. (I can only tear along the perforations separating adjacent stamps, and each block must come out of a sheet in one piece.) Let be the smallest number of blocks I can tear out and make it impossible to tear out any more blocks. Prove that there are real constants and such that
for all .
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions