Thread: Quickie #12

For what is a square?

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)

Hello, AfterShock!

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.