I started studying continued fractions..., a vast subject. ( 'new land!' )

Here I calculate the Extended GCD of $9976$ and $6961$ using Blankinship's matrix method. A by-product of the calculation ( column 1 ) are the numbers for expressing $\frac{9976}{6961}$ as a finite continued fraction.

$\left(

\begin{array}{cccc}

- & - & 9976 & 6961 \\

- & 9976 & 1 & 0 \\

1 & 6961 & 0 & 1 \\

2 & 3015 & 1 & -1 \\

3 & 931 & -2 & 3 \\

4 & 222 & 7 & -10 \\

5 & 43 & -30 & 43 \\

6 & 7 & 157 & -225 \\

7 & 1 & -972 & 1393\\

& 0 & 6961 & -9976 \\

\end{array}

\right)$

$\frac{9976}{6961}=1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5+\frac{1}{6+\frac{1}{7}}}}}}$

2-2018 Teaching by misleading

4 months ago

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