# simple Pell's Equation

• May 3rd 2009, 02:14 AM
Aquafina
simple 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 AM
Moo
Hello,
Quote:

Originally Posted by Aquafina
hi

i need to solve the pell's equation

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

but i dont know how to do them..

See here : http://www.imomath.com/tekstkut/pelleqn_ddj.pdf
Your equation is the Example 1.

• May 3rd 2009, 03:28 AM
Aquafina
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 AM
Aquafina
basically, i need all integer solutions, can i say this is an infinite number?
• May 3rd 2009, 12:32 PM
ThePerfectHacker
If $t_n$ is a square then $t_{4n(n+1)}$ is a square.
Thus, there are infinitely many solutions.
• May 3rd 2009, 08:42 PM
Aquafina
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