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(ax + b)/x=(Ax + B)/Cx \in Q (HOMC 2013 J Q15)

Source:

July 28, 2019

rationalalgebra

Problem Statement

Denote by

Q

and

N^*

the set of all rational and positive integer numbers, respectively. Suppose that

\frac{ax + b}{x} \in Q

for every

x \in N^*

: Prove that there exist integers

A,B,C

such that

\frac{ax + b}{x}= \frac{Ax + B}{Cx}

for all

x \in N^*