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# An Algebraic View on Continued Fraction Factorization

Consider the field

Looking at the determinant of

we see that and thus . Let . Then . It is clear that there seems to be a correspondence between and . Thus one could consider the factorization of by considering the factorizatino of in .

A unit in is a number of the form . A number in is said to be prime if implies that or is a unit. Let be such numbers. Then we can look at the factorization

 (13)

This correspondence between prime factorization in and the factorization of continued fractions could be an area for further research.

scanez 2000-12-04