2002 IMO Problems
Problems of the 2002 IMO.
Contents
Day I
Problem 1
is the set of all with non-negative integers such that . Each element of is colored red or blue, so that if is red and , then is also red. A type subset of has blue elements with different first member and a type subset of has blue elements with different second member. Show that there are the same number of type and type subsets.
Problem 2
is a diameter of a circle center . is any point on the circle with . is the chord which is the perpendicular bisector of . is the midpoint of the minor arc . The line through parallel to meets at . Show that is the incenter of triangle .
Problem 3
Find all pairs of positive integers for which here exist infinitely many positive integers such that
is itself an integer.
Day II
Problem 4
Let be an integer and let be all of its positive divisors in increasing order. Show that
Problem 5
Find all functions such that
for all real numbers .
Problem 6
Let be a positive integer. Let be unit circles in the plane, with centers respectively. If no line meets more than two of the circles, prove that
See Also
2002 IMO (Problems) • Resources | ||
Preceded by 2001 IMO |
1 • 2 • 3 • 4 • 5 • 6 | Followed by 2003 IMO |
All IMO Problems and Solutions |