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Vieta jumping : ウィキペディア英語版
Vieta jumping
In number theory, Vieta jumping, also known as root flipping, is a proof technique. It is most often used for problems in which a relation between two positive integers is given, along with a statement to prove about its solutions. There are multiple methods of Vieta jumping, all of which involve the common theme of infinite descent by finding new solutions to an equation using Vieta's formulas.
== History ==
Vieta jumping is a relatively new technique in solving mathematical olympiad problems, as the first olympiad problem to use it in a solution was proposed in 1988 for the International Mathematics Olympiad and assumed to be the most difficult problem on the contest. Arthur Engel wrote the following about the problem difficulty:
George Szekeres' wife, mentioned in the above quote, is Esther Klein. Among the eleven students receiving the maximum score for solving this problem, there was the future Fields-medallist Ngô Bảo Châu.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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