**Continued Fractions**

*p*_{k+1} = a_{k+1}*p*_{k} + *p*_{k-1}, and

*q*_{k+1} = a_{k+1}*q*_{k} + *q*_{k-1}

*p*_{-2} = *q*_{-1} = 0 and

*p*_{-1} = *q*_{-2} = 1

Leveque, James. __Fundamentals of Number Theory__. See http://www.amazon.com/exec/obidos/tg/detail/-/0486689069/

qid=1074367205//ref=sr_8_xs_ap_i0_xgl14/002-8476672-9958465?v=glance&s=books&n=507846.

Davenport, H. The Higher Arithmetic. See http://www.amazon.com/exec/obidos/tg/detail/-/0486689069/

qid=1074367205//ref=sr_8_xs_ap_i0_xgl14/002-8476672-9958465?v=glance&s=books&n=507846.

Most information in the writeup comes from personal knowledge gleaned from various sources over the years. However, the above references are either very helpful, well-written, highly-recommended, or several of these things.