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Factorial-Like Product

Source: AIME 2010II Problem 3

April 2, 2010
factorialAMCnumber theory

Problem Statement

Let K K be the product of all factors (b\minus{}a) (not necessarily distinct) where a a and b b are integers satisfying 1≤a<b≤20 1\le a < b \le 20. Find the greatest positive integer n n such that 2n 2^n divides K K.
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