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This is the last problem of the semester. Enjoy your summer break. I will try to post solutions over the summer as I am able. Many thanks for your kind wishes over the last several weeks. I look forward to more problems (and solutions) when we return in the fall.
This problem appeared in the Student Mathematics Competition of the Illinois Section of the Mathematical Association of America which took place on April 2, 2004. Congratulations to Bradley University students Jeremy Light, Chris Mossell, Tim Roberts who came in first among university teams. Congratulations!
Find positive integers a1, a2, ... , an whose sum is 100 and whose product a1a2 ... an is maximal over every possible choice of n and every possible choice of a1, a2, ... , an.
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ã2004 Alberto L. Delgado