Your equation is the Example 1.
I hope this will help you understand...
i've actually used the substitution
x=2n+1 and y=2m
im basically showing the solutions of how many triangular numbers are also square
so will i have to substitute these back into the equation, or can i just say there are infite many solutions to x^2 - 2y^2 =1 so infinite many trianglular square numbers?
sorry i didnt understand the notation you used:
"If is a square then is a square..."
what numbers are these?
also, if you say there are infinite integer solutions, then there are infinite triangular square numbers..
so are there infinite pentagonal square numbers?
i.e. as shown on this link: Pentagonal Square Number -- from Wolfram MathWorld