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Simple Continued Fraction

A Continued Fraction

\sigma=a_0+{\strut\displaystyle b_1\over{\strut\displaystyle...
...\strut\displaystyle b_3\over\strut\displaystyle a_3+\ldots}}}}
\end{displaymath} (1)

in which the $b_i$s are all unity, leaving a continued fraction of the form
\sigma = a_0+{1\over{\strut\displaystyle a_1+{\strut\display...
...{\strut\displaystyle 1\over\strut\displaystyle a_3+\ldots}}}}.
\end{displaymath} (2)

A simple continued fraction can be written in a compact abbreviated Notation as
\sigma=[a_0, a_1, a_2, a_3, \ldots].
\end{displaymath} (3)

Bach and Shallit (1996) show how to compute the Jacobi Symbol in terms of the simple continued fraction of a Rational Number $a/b$.

See also Continued Fraction


Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.

© 1996-9 Eric W. Weisstein