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Is it possible to solve the equation $3a^2=2b^2+1$ for positive, integral $a$ and $b$ using recurrences?I am sure it is, as Arthur Engel in his Problem Solving Strategies has stated that as a method, but I don't think I understand what he means.Can anyone please tell me how I should go about it?Thanks. Edit:Added the condition that $a$ and $b$ are positive integers.

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Which part? Which page? Section? –  J. M. Nov 13 '11 at 15:55
    
Page number 154, solution to Problem 137 in the number theory section. –  Eisen Nov 13 '11 at 16:01
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See also page 147, solution of 92(b). Both occurrences are after Pell's equation. –  Martin Sleziak Nov 13 '11 at 16:04
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If you have access to this book, Section 3.2 Solving Pell's Equation in the book An Introduction to Diophantine Equations: A Problem-Based Approach By Titu Andreescu, Dorin Andrica, Ion Cucurezeanu should contain more than enough information on Pell's equation. See p.121. Maybe you don't even have to go through the proofs, it should be enough if you understand what the results claim and practice them on a few concrete examples. –  Martin Sleziak Nov 13 '11 at 16:14
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Other useful resources to learn about Pell's equation could be: imomath.com/tekstkut/pelleqn_ddj.pdf, artofproblemsolving.com/Wiki/index.php/Pell_equation and, of cousrse, wikipedia. And, very probably, for solution of this exercises the facts mentioned in Engel's book should be sufficient. –  Martin Sleziak Nov 13 '11 at 16:30

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