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No other case (Posted on 2015-02-24) Difficulty: 3 of 5
1!+2!+3!=9=32.

Prove that k=3 is the only case of the sum 1!+2!+3!+...k! resulting in an integer power of an integer number.

No Solution Yet Submitted by Ady TZIDON    
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The easy half | Comment 1 of 2
k=4 gives 33
Every factorial above 4 ends in 0 so the sum will end in 3.
No perfect square ends in 3, so that rules out any even power.

Of course, odd powers can end in 3.

  Posted by Jer on 2015-02-24 12:13:27
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