Another number theory problem.
I can find the small value of $b$ such that 0,1,2.
But, I cannot find the upper limit of $b$, such that the value of $b$ is limited.
How can I find the solution $(a,b)$ from this problem?
Thanks
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If $b$ is even, then $a = b/2$ always works... – Arthur Jun 16 '14 at 16:26
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also $b \leq 2a$ for the expression to be positive. – Anurag A Jun 16 '14 at 16:29
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5This is IMO 2003 problem. You can check the solutions on AOPS – Stefan4024 Jun 16 '14 at 16:34
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And how to be with the decisions of which are determined by the equations Pell? – individ Jun 16 '14 at 16:53
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Use so-called "Vieta jumping", i.e. descent by reflection on integer points of a conic. – Bill Dubuque Jun 16 '14 at 16:56
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How can we related this form with Pell equations or 'Vieta Jumping'? Are they related? I just heard the word 'Vieta jumping' today. Thanks – akusaja Jun 16 '14 at 16:59
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This does two different methods. – individ Jun 16 '14 at 17:04