From CS2800 wiki
(Redirected from Bézout coefficients)
Bézout coefficients of and .and satisfying this equation are called
We will do this proof by induction. Since the inductive principle used to define uses strong induction on the second argument, we will use the same inductive principle for the proof. Let be the statement "for all , there exists such that ." We will prove and assuming for all .
To see choosing and gives the result we want., we have . Thus
Note that we could choose different values for Bézout coefficients are not necessarily unique.; this shows that the
if we let and .