Problem :
find the smallest natural number $n>1$ such that :
$$n(n+1)(2n+1)=6m^{2}~~,m\in\mathbb{N}$$
I don't know the method to find $n$ but I try many time
$$n=1,2,3,....,24$$
Then I find $n=24$
$$24.25.49=6.70^{2}$$
Another try :
$$n\equiv r\pmod{6}~~,r=1,..,5$$
$n=6k$ then $k(6k+1)(12k+1)=m^{2}$
So $k,6k+1,12k+1$ is perfect square in same time I find $k=4$ so $n=24$ Also for all $n=6k+r$ I can't find $n$ ?
So I'm going to see you solution Thanks!