2003 Pan African MO Problems
Contents
Day 1
Problem 1
Let . Find all functions: such that:
(1) , all ;
(2) ;
(3) , all .
Problem 2
The circumference of a circle is arbitrarily divided into four arcs. The midpoints of the arcs are connected by segments. Show that two of these segments are perpendicular.
Problem 3
Does there exists a base in which the numbers of the form: are all prime numbers?
Day 2
Problem 4
Let . Does there exist a function such that: where we define: and , ?
Problem 5
Find all positive integers such that divides .
Problem 6
Find all functions such that: for .
See Also
2003 Pan African MO (Problems) | ||
Preceded by 2002 Pan African MO |
1 • 2 • 3 • 4 • 5 • 6 | Followed by 2004 Pan African MO |
All Pan African MO Problems and Solutions |