3. Repeating sequence of continued fraction
Continued fraction expansion and the solutions of Pell equation
Computing the solutions of Pell equation for n less than 100.
- integer part, length of fraction part,
fraction part for continued fraction expansion of sqrt(n)
- solutions of Pell equation
- x2 - my2
Results of computation are here.
the pattern of fraction part of continued fraction of sqrt(n) is always palindromic as
a1, a2, ...... , ai, ...... , a2, a1, b
last "b" is twice of integer part
- right part of Pell equation's value is (-1) k where k is the length of fraction part
- sqrt(n2+1) = n [2n]
- sqrt(n2+2) = n [n, 2n]
Excel work sheet for solving the Pell equation
E-mail : email@example.comHisanori Mishima