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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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Some Thoughts Smallest divisor Comment 8 of 8 |
OEIS A055204 is the sequence of the squarefree part of n!  The 50th term of this sequence is 71661341518. This then implies that (1!*2!*3!*4!* ... 100!)/71661341518 is a perfect square, specifically the largest square possible.
  Posted by Brian Smith on 2017-09-08 23:21:36
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