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Divisible by a Dozen

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Author: Terry Trotter & Annie Fetter
Description: teacher support live problem Pre-Algebra, difficulty level 3. If you take any three consecutive integers, multiply the first times the square of the second, then multiply by the third, is 12 a factor of the product?
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Problem page: http://mathforum.org/librarypow/puzzles/index2.ehtml?puzzle=2960
Support page: http://mathforum.org/pow/support/prealg/20030908pre.teacher.html
Solution page: Problem #2960

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