hi

i need to solve the pell's equation

http://mathworld.wolfram.com/images/...dEquation2.gif

but i dont know how to do them..

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- May 3rd 2009, 02:14 AMAquafinasimple Pell's Equation
hi

i need to solve the pell's equation

http://mathworld.wolfram.com/images/...dEquation2.gif

but i dont know how to do them.. - May 3rd 2009, 02:51 AMMoo
Hello,

See here : http://www.imomath.com/tekstkut/pelleqn_ddj.pdf

Your equation is the Example 1.

I hope this will help you understand... - May 3rd 2009, 03:28 AMAquafina
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? - May 3rd 2009, 03:30 AMAquafina
basically, i need all integer solutions, can i say this is an infinite number?

- May 3rd 2009, 12:32 PMThePerfectHacker
If $\displaystyle t_n$ is a square then $\displaystyle t_{4n(n+1)}$ is a square.

Thus, there are infinitely many solutions. - May 3rd 2009, 08:42 PMAquafina
sorry i didnt understand the notation you used:

"If http://www.mathhelpforum.com/math-he...c30deb2c-1.gif is a square then http://www.mathhelpforum.com/math-he...5fecf7d5-1.gif 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