(1) |

Now we prove . Assume and let is a solution of Equation (2). Since , then and are coprime. Let be in . Then we have

Finally, we prove . Let be a solution of Equation (2). Let and be the quotient and the remainder of w.r.t. . Hence we have

We define

(7) |

Observe that

solves Equation (2) too. By Relation (6) and by hypothesis we have

leading to

Therefore we have

This proves the existence. Let us prove the unicity. Let be a solution of Equation (2). We know that there exists such that . Since holds, if , we have

This implies the uniquemess.

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2008-01-07