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2006 AMC 10BProblem 18P16-20~3 minPrint
Sequences & SeriesModular ArithmeticCompute small cases, spot the pattern, generalize

Let a1,a2,...a_1 , a_2 , ... be a sequence for which a1=2a_1=2 , a2=3a_2=3 , and an=an−1an−2a_n=\frac{a_{n-1}}{a_{n-2}} for each positive integer n≥3n \ge 3 . What is a2006a_{2006} ?

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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.