1. ## simple Pell's Equation

hi

i need to solve the pell's equation

but i dont know how to do them..

2. Hello,
Originally Posted by Aquafina
hi

i need to solve the pell's equation

but i dont know how to do them..
See here : http://www.imomath.com/tekstkut/pelleqn_ddj.pdf
Your equation is the Example 1.

3. thanks!

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?

4. basically, i need all integer solutions, can i say this is an infinite number?

5. If $\displaystyle t_n$ is a square then $\displaystyle t_{4n(n+1)}$ is a square.
Thus, there are infinitely many solutions.

6. 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