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Math Help - simple Pell's Equation

  1. #1
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    simple Pell's Equation

    hi

    i need to solve the pell's equation



    but i dont know how to do them..
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  2. #2
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    Hello,
    Quote Originally Posted by Aquafina View Post
    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.

    I hope this will help you understand...
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  3. #3
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    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?
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  4. #4
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    basically, i need all integer solutions, can i say this is an infinite number?
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  5. #5
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    If t_n is a square then  t_{4n(n+1)} is a square.
    Thus, there are infinitely many solutions.
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  6. #6
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    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
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