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(ax + b)/(cx+d)=(Ax + B)/(Cx+D) \in Q (HOMC 2013 Q15)

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August 1, 2019
algebrarational

Problem Statement

Denote by QQ and N∗N^* the set of all rational and positive integer numbers, respectively. Suppose that ax+bcx+d∈Q\frac{ax + b}{cx + d} \in Q for every x∈N∗x \in N^*: Prove that there exist integers A,B,C,DA,B,C,D such that ax+bcx+d=Ax+BCx+D\frac{ax + b}{cx + d}= \frac{Ax + B}{Cx+D} for all x∈N∗x \in N^*
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