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Removing a factorial to form a square

Source: OMK 2015 Sulong, Section B Problem 3

June 21, 2021
number theoryfactorial

Problem Statement

There are 200200 numbers on a blackboard: 1!,2!,3!,4!,......,199!,200! 1! , 2! , 3! , 4! , ... ... , 199! , 200!. Julia erases one of the numbers. When Julia multiplies the remaining 199199 numbers, the product is a perfect square. Which number was erased?
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