[seqfan] Re: three triangular numbers in a row

[Georgi Guninski]

On Fri, Jun 24, 2011 at 01:58:37PM +1000, Brendan McKay wrote:
> A question related to A075528 and A061278 was asked at
>    http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Mathematics#Striped_triangle_question
> 
> It is equivalent to: 
>    Is there any n such that n, 2n, and 3n are all triangular numbers?
> 
> Brendan.
>
I would recommend the question to be asked on http://math.stackexchange.com/
or http://mathoverflow.net/

Might help to add that over the rationals the equations define an elliptic curve so it boils down to finding the integral points.

I tried to solve it, but can't get a Weierstrass model (for the group law) because of a program bug...

Possibly the OP disallows non-positive n because of (0,0,-1).

-- 
joro