# Dividing sequences

Algebra Level pending

Tom takes two sequences $$\{1 , 9 , 36 , 100 , 225 , 441\}$$ and $$\{1 , 5 , 14 , 30 , 55 , 91\}$$. Tom divides the $$n^\text{th}$$ term of the first sequence by the $$n^\text{th}$$ term of the second sequence. For how many values of $$n$$ is the result an integer?

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