2
$\begingroup$

If I have a continued fraction for an irrational number $z= \langle a_0;a_1,a_2,a_3,\ldots\rangle$ it seems that $(-1)*z = \langle-a_0;-a_1,-a_2,-a_3,\ldots\rangle$. Is this true?

In general, if you have the continued fraction representation for $y$ and $z$ can you say something about the continued fraction representation of $y*z$?

  • 0
    I fixed your LaTeX. Note that you should include entire formulas in between dollar signs, not parts of them: write `$z= \langle a_0;a_1,a_2,a_3,\ldots\rangle$`. Also, due to html you should not use `<` and `>`, rather use `$\lt$` and `$\gt$`.2011-11-15
  • 4
    Maybe you should give a definition of **the** continued fraction representation.2011-11-15
  • 0
    http://www.inwap.com/pdp10/hbaker/hakmem/cf.html2011-11-15
  • 1
    Phira is probably hinting to you that "continued fraction" is commonly interpreted to mean "regular continued fraction" and that means that $a_1,a_2,\dots$ must all be positive, so your fraction for $-z$ doesn't qualify.2011-11-15

2 Answers 2