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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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re: The easy half / another third Comment 2 of 2 |
(In reply to The easy half by Jer)

My previous comment is basically dealing with mod 10 to rule out squares.

I haven't found a method that works for all prime powers, but with different moduli one can rule out different powers.

For example, using mod 7, it's easy to rule out cubes.

  Posted by Jer on 2015-02-25 10:43:51
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