| 1. Prove that there is just one solution in integers m > n to 2/p = 1/m + 1/n for p an odd prime. |
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| 2. Show that an odd square cannot be expressed as the sum of five odd squares. |
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| 3. Find the point P on the line AB which maximizes 1/(AP + AB) + 1/(BP + AB). |
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The original problems are in Hungarian. They are available on the KöMaL archive on the web. They are also available in English (with solutions) in: Andy Liu, Hungarian Problem Book III, 1929-1943, MAA 2001. ISBN 0883856441.
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© John Scholes
jscholes@kalva.demon.co.uk
6 January 2003
Last corrected/updated 3 Nov 03