perplexus.info :: Just Math : No other case

No other case (Posted on 2015-02-24)

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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

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

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info