MathDB

The fraction f(x)/g(x) [Iran Second Round 1993]

Source: 1993 Iran Second Round

November 25, 2010

algebrapolynomialratioalgebra proposed

Problem Statement

Let

f(x)

and

g(x)

be two polynomials with real coefficients such that for infinitely many rational values of

x

, the fraction

\frac{f(x)}{g(x)}

is rational. Prove that

\frac{f(x)}{g(x)}

can be written as the ratio of two polynomials with rational coefficients.