## Number Theory: Lecture 23

In which we encounter some methods for factorising a large number.

• Description of Fermat factorisation.
• Definition of least absolute residue.  (See also Gauss’s lemma, in lecture 7.)
• Definition of a factor base and of a $B$-number.
• Description of the factor-base method.

As we saw, the factor-base method relies on coming up with a suitable factor base $B$ and suitable $B$-numbers.  How could continued fractions help us with this?