Introduction to polynomial continued fractions

Ofir David

Published 2023-08-03Version 1

The simple continued fraction expansion is a basic and powerful tool in number theory. However, finding the actual coefficients in the expansion is usually quite hard, since we need to compute each coefficient one after the other using the generalized Euclidean division algorithm. In this note we introduce the polynomial continued fraction expansion, which while lacks some of the interesting properties the simple continued fraction expansions have, in return we gain much simpler formulas and easier computation which lead by themselves to other interesting results.