... to as a divisor of a, and a is called a multiple of b The relation bJa is reflexive and transitive but not symmetric; in fact if bla and alb then a = b Clearly also if b (a then b s a and SO a ... for all rationals p/q (q > 0) For the proof, we shall assume, as clearly we may, that a is real, and we shall apply the mean-value theorem to P, the minimal polynomial for a We have, for any rational ... point, and similarly that the tangent at a rational point intersects again at a rational point Thus, Fermat remarked, if there is a rational point on the curve other than the point at infinity, then,...