Divisible by this year? (Part 3: What if I did this?)

Number Theory Level 5

\(n!\) or \(n\)-factorial is the product of all integers from \(1\) up to \(n\) \((n! = 1 \times 2 \times 3 \times ... \times n)\). Let's denote \(n!!\) be the product of all factorials from \(1!\) up to \(n!\) \((n!! = 1! \times 2! \times 3! \times ... \times n!)\). Find the maximum integral value of \(k\) such that \(2014^k\) divides \(2014!!\)

You may also try these problem:

Divisible by this year???

Divisible by this year??? (Part 2: Factorials)


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