In the Exercise $9$, page 16, from Burton's book Elementary Number Theory he state the following:
Establish the identity $t_{x}=t_{y}+t_{z},$ ($t_{n}$ is the nth triangular numbers) where ${x}=\frac{n(n+3)}{2}+1\,\,\,\,\,\,\,y=n+1\,\,\,\,\,\,\,z=\frac{n(n+3)}{2}$ and $n\geq 1,$ thereby proving that there are infinitely many triangular numbers that are the sum of two other such numbers.
I tried to find out how did he get $x,y$ and $z$ but I've failed. I wrote $\frac{y(y+1)}{2}+\frac{z(z+1)}{2}=\frac{x(x+1)}{2}$ but I don't know what to do from now on. How one can find $x,y,z$ as above?
I would appreciate your help.