MathForces: Math Olympiads
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Author: mathforces
Problem has been solved: 16 times

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A group of 16 friends take turns choosing random integer numbers. The first of them randomly selects the number $ a_1 $ on the segment $ [0,1] $, the second - the number $ a_2 $ on the segment $ [0,2] $, the third - the number $ a_3 $ on the segment $ [0,3] $, and so on. Let the probability that the sequence of numbers $ a_1, a_2, ..., a_{16} $ is strictly increasing is equal to $ \frac {a}{b} $, where $ a $ and $ b $ are coprime positive integer numbers. Find the number of divisors of the product $ ab $.





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