| 1. m and n are odd. Show that 2k divides m3 - n3 iff it divides m - n. |
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| 2. Let a right angled triangle have side lengths a > b > c. Show that for n > 2, an > bn + cn. |
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| 3. Let the vertices of a regular 10-gon be A1, A2, ... , A10 in that order. Show that A1A4 - A1A2 is the radius of the circumcircle. |
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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): (Translated by Elvira Rapaport) József Kürschák, G Hajós, G Neukomm & J Surányi, Hungarian Problem Book 2, 1906-1928, MAA 1963. Out of print, but available in some university libraries.
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John Scholes
jscholes@kalva.demon.co.uk
20 Oct 1999