Pell's equation

English Alternative forms en Pell equation Etymology Named by Leonhard Euler after the 17th-century mathematician John Pell, whom Euler mistakenly believed to be the first to find a general solution.Earliest Known Uses of Some of the Words of Mathematics (P) Noun en number theory The Diophantine equation for a given integer m, to be solved in integers x and y. en 1974 Allan M. Kirch Elementary Number Theory: A Computer Approach Intext Educational Publishers https://books.google.com.au/books?id=tAgGa_k040AC&q=%22Pell%27s+equation%22%7C%22Pell%27s+equations%22&dq=%22Pell%27s+equation%22%7C%22Pell%27s+equations%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjC_PS6zPDuAhW7IbcAHTg7BOoQ6AEwB3oECC4QAg 212 However, due to Euler's mistake in attributing the equation to English mathematician John Pell (1610-1585), Equation (27.14) is called Pell's equation. Results concerning Pell's equation will be stated without proof. en 1989 Mathematics Magazine, Volume 62 w:Mathematical Association of America https://books.google.com.au/books?id=_783AAAAIAAJ&q=%22Pell%27s+equation%22%7C%22Pell%27s+equations%22&dq=%22Pell%27s+equation%22%7C%22Pell%27s+equations%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjC_PS6zPDuAhW7IbcAHTg7BOoQ6AEwDHoECDgQAg 258 Thus satisfies Pell's equation and so by Lemma 1, is a convergent to . en 2013 John J. Watkins Number Theory: A Historical Approach https://books.google.com.au/books?id=lGmYDwAAQBAJ&pg=PA409&dq=%22Pell%27s+equation%22%7C%22Pell%27s+equations%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjC_PS6zPDuAhW7IbcAHTg7BOoQ6AEwA3oECCQQAg#v=onepage&q=%22Pell's%20equation%22%7C%22Pell's%20equations%22&f=false 409 w:Princeton University Press We introduced Pell's equationin Chapter 4 as an example of a Diophantine equation. The solution of the Pell equation was used in India in the fourth century to produce the fraction as an excellent rational approximation for .It is easy to see why solutions to Pell's equation can be used to approximate solutions to —this was known to Archimedes, who used this method to approximate square roots. Synonyms en Pell-Fermat equation Derived terms en generalised Pell's equation Related terms en Pell number Translations Diophantine equation German: de Pellsche Gleichung f Italian: it equazione di Pell f Polish: pl równanie Pella n References Further reading Pell number en eponyms