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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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miscellany | Comment 6 of 8 |
(In reply to re: when it works -- computer exploration please edit by Ady TZIDON)

I've corrected the "n/2" to "(n/2)!", as pointed out by Ady.


I've finally understood chun's solution.  I probably could have understood it earlier if an intermediate result had not been left out:

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

before the final equality.  Students need the teacher to avoid leaving out intermediate steps, though some catch on faster.

  Posted by Charlie on 2017-09-08 08:51:28
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