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A bigger product made integer

Source: Problem 5 of Russian Regional Olympiad 2011, grade 10/11

September 1, 2011
number theory proposednumber theory

Problem Statement

Find all aa such that for any positive integer nn, the number an(n+2)(n+3)(n+4)an(n+2)(n+3)(n+4) is an integer. (Author: O. Podlipski) [url=http://www.artofproblemsolving.com/Forum/viewtopic.php?f=57&t=427802](similar to Problem 5 of grade 9) Same problem for grades 10 and 11
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