E559 -- Nova subsidia pro resolutione formulae \(axx + 1 = yy\)

(New assistance for solving the formula \(axx + 1 = yy\))


This describes Euler's solution of the Pell equation without the use of continued fractions. It opens with the biggy: if \(a = 61\), then \(x = 226,\!153,\!980\) and \(y = 1,\!766,\!319,\!049\). Euler includes the following problems: According to the records, it was presented to the St. Petersburg Academy on September 23, 1773.

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