Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 687. (January 2017)

A. 687. Let $\displaystyle f(x)$ and $\displaystyle g(x)$ be nonzero polynomials such that the degree of $\displaystyle f(x)$ is higher than that of $\displaystyle g(x)$. Suppose that for infinitely many prime numbers $\displaystyle p$, the polynomial $\displaystyle pf(x)+g(x)$ also has a rational root. Show that $\displaystyle f(x)$ has a rational root.

(Italian problem)

(5 pont)

Deadline expired on February 10, 2017.

### Statistics:

 4 students sent a solution. 5 points: Lajkó Kálmán, Williams Kada. 4 points: Bukva Balázs, Matolcsi Dávid.

Problems in Mathematics of KöMaL, January 2017