| 1. Show that there are no integers n such that n4 + 4n is a prime greater than 5. | |
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2. ABC is a triangle with orthocenter H. The median from A meets the circumcircle again at A1, and A2 is the reflection of A1 in the midpoint of BC. The points B2 and C2 are defined similarly. Show that H, A2, B2 and C2 lie on a circle.
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| 3. Three schools each have n students. Each student knows a total of n+1 students at the other two schools. Show that there must be three students, one from each school, who know each other. |
The original problems are in Hungarian. Many thanks to Péter Dombi for the translation.
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(C) John Scholes
jscholes@kalva.demon.co.uk
19 Apr 2003
Last corrected/updated 19 Apr 2003