TABLE OF CONTENTS We presume that the reader is already familiar with the notions of modulo n calculations, 
field, p prime (also noted 
) and Euclid and Bezout equalities. We also presume that the concept of ring of polynomials on the 
field is also known. An important result concerning the ring of polynomials is the following.
Any non-zero polynomial of degree n has at most n roots in a field.
| Proof | The proof is outside the scope of this book. |
A useful result for us is provided in the following proposition.
If ? is a root of a polynomial f( X) of 
, then ? 2 is also a root.
| Proof | Let us pose |
Let us suppose a polynomial 
. The set noted 
is the set of polynomial expressions in X, with coefficients in 
, where we add and multiply two elements calculating in 
then taking the remainder of the division of the result by a( X). We...
