2003 Pan African MO Problems
Let . Find all functions: such that:
(1) , all ;
(3) , all .
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.
Does there exists a base in which the numbers of the form: are all prime numbers?
Let . Does there exist a function such that: where we define: and , ?
Find all positive integers such that divides .
Find all functions such that: for .
|2003 Pan African MO (Problems)|
2002 Pan African MO
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2004 Pan African MO
|All Pan African MO Problems and Solutions|