For what is a square?
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Originally Posted by Soroban For what is a square? Certainly for 1, 3, although for all n in general I'd start by using the fact
n^2 = summation(2k-1, k = 1...n)
and go from there.
I have a feeling 20 is one...
Originally Posted by anthmoo I have a feeling 20 is one... No, 20 is not one. I checked with Maple.
You end up with 33sqrt(2.3519995354562*10^15)
You found the only two solutions . . .
Note that squares must end in:
List the first few sums:
Since all end in , . . all subsequent sums will end in . . and hence cannot be squares.
Therefore: are the only solutions.
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