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Product of 100 factorials (Posted on 2017-09-07) Difficulty: 4 of 5
Show that (1!*2!*3!*4!* ... 100!)/50! is a square number.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.5000 (2 votes)

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Solution Solution | Comment 1 of 8

Rearrange:  (1!*2!*3!*4!* ... 100!)/50!

= (1!*2!/1)*(3!*4!/2)*(5!*6!/3))*(7!*8!/4)*......*(97!*98!/49)*(99!*100!/50)

= [(1!)^2 * (3!)^2 * (5!)^2 * (7!)^2 * ...... * (97!)^2 * (99!)^2] * 2^50

This is a product of 51 square numbers.


Edited on September 7, 2017, 9:05 am
  Posted by chun on 2017-09-07 09:01:22

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