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View Full Version : Pell equation: looking for simpler proof, or help w/ book's



luckyc1423
04-13-2007, 08:18 PM
I am doing a research type paper in my capstone course...I have this proof I need to solve, actually, the book solves the proof for me but I am not following what they are doing...I wanted to post it here and hopefully someone knows a simplier version to do this and maybe I will understand your version

Nontrivial solution of the pell equation: When n is a non square positive integer, the equation x^2 - n(y^2) = 1

stapel
04-13-2007, 08:33 PM
...hopefully someone knows a simplier version....
How many proofs have you looked at online (http://www.google.com/search?hl=en&q=solve+%22pell+equation%22)?

Eliz.

luckyc1423
04-13-2007, 08:43 PM
I couldnt find one online that either delt with the specific requirements I have on the proof or I dont understand it...I have been on planetmath.com and all the other websites

luckyc1423
04-13-2007, 08:47 PM
I dont know if it matters but im trying to prove the non trivial solutions meaning not equal to +- 1

stapel
04-13-2007, 11:50 PM
I couldnt find one online that...[dealt] with the specific requirements I have....
Then it might be helpful if you spelled out what those requirements are.

Please be complete and specific. Thank you.

Eliz.

luckyc1423
04-14-2007, 01:16 AM
its just that (a,b) cannot equal (+ or - 1, 0)

stapel
04-14-2007, 08:16 AM
its just that (a,b) cannot equal (+ or - 1, 0)
I'm sorry but, out of context, this has no meaning.

Please reply with the full text of the proof you don't care for, along with a clear explanation of the bits for which you would like clarification and/or simplification.

Thank you.

Eliz.

luckyc1423
04-14-2007, 09:31 AM
That is the requirements, I just assumed the proof had to be different because its non trivial
so (a,b) cannot equal (+ or - 1, 0)
a cannot be (+ or -) 1 and b cannot b 0

The proofs found the google are somewhat confusing

Do you have a more simplified version?

pka
04-14-2007, 09:56 AM
Look at this link:
http://www.mathhelpforum.com/math-help/urgent-homework-help/13578-pell-equation-pigeonhole-argument.html
Does that help?

luckyc1423
04-14-2007, 11:46 AM
That is a different proof, that is the proof of the approximation...I found a few proofs on the pell equation online just confusing...usually people on these forums have versions that are easy to understand