| 1. Can you find an infinite set of positive integers such that each pair has a common divisor (greater than 1), no integer (greater than 1) divides all members of the set, and no member of the set divides any other member? | |
| 2. Show that there is a polynomial with integer coefficients whose values at 1, 2, ... , n are different powers of 2. | |
| 3. For which n > 2 can we find n points in the plane, no three collinear, so that for each triangle of the points which are in the convex hull, exactly one of the points belongs to its interior. |
The original problems are in Hungarian. Many thanks to Péter Dombi for the translation.
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John Scholes
jscholes@kalva.demon.co.uk
20 May 2002
Last corrected/updated 19 Apr 03