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2003 AMC 10BProblem 18P16-20~3 minPrint
Divisibility & FactorsNumber PropertiesUse the answer choices (mod checks, size, form) to eliminate or selectTest small/specific values or special cases to find or verify the answer

What is the largest integer that is a divisor of

(n+1)(n+3)(n+5)(n+7)(n+9)(n+1)(n+3)(n+5)(n+7)(n+9)

for all positive even integers nn ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2003 12B #12.