[seqfan] Re: Problem submitting a sequence

Max Alekseyev maxale at gmail.com
Sat Nov 5 17:40:42 CET 2011

On Fri, Nov 4, 2011 at 6:31 PM, Alonso Del Arte
<alonso.delarte at gmail.com> wrote:
> Would that be numbers that are both triangular and decagonal? Al

If a number m is triangular then 4m+1 is a square.
If a number m is decagonal then 16m+9 is a square.

Hence we have a system of equations:
4m+1 = x^2
16m+9 = y^2
which implies
y^2 - 4x^2 = 5
that is
implying that the only solution in nonnegative x,y is (x,y)=(1,3).

Therefore, there is the only number that is both triangular and
decagonal which is 0.


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