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I know the Vieta Jumping method started to be used in Mathematics Olympiads in the IMO of 1988. But I'd like to know the history of this method before being used in mathematics olympiads. Where did it first come from? References (books)? Has this method already existed in the literature before appearing in olympiads?

danilocn94
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A better version occurs in a 1907 article by Hurwitz. I ought to emphasize that there are two basic flavors, given $M > 0$ and $m > 0.$ One is $$ x^2 - M xy + y^2 = m, $$ the other is $$ x^2 - Mxy + y^2 = -m. $$ Not quite the same outcome.

Showing that $m^2-n^2+1$ is a square

Showing that $m^2-n^2+1$ is a square

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Will Jagy
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  • Is this the only occurrence of this method in the literature before the IMO of 1988? How did eleven high school students know this method and knew how to answer correctly the question that appeared in this IMO? – danilocn94 Mar 27 '17 at 00:20