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In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent. It is named after Srinivasa Ramanujan, who conjectured that it has only five integer solutions, and after Trygve Nagell, who proved the conjecture. ==Equation and solution== The equation is : and solutions in natural numbers ''n'' and ''x'' exist just when ''n'' = 3, 4, 5, 7 and 15. This was conjectured in 1913 by Indian mathematician Srinivasa Ramanujan, proposed independently in 1943 by the Norwegian mathematician Wilhelm Ljunggren, and proved in 1948 by the Norwegian mathematician Trygve Nagell. The values on ''n'' correspond to the values of ''x'' as:- :''x'' = 1, 3, 5, 11 and 181.〔Saradha & Srinivasan (2008) p.208〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ramanujan–Nagell equation」の詳細全文を読む スポンサード リンク
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