2003 Pan African MO Problems
Contents
[hide]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 |