Mathematical and Physical Journal
for High Schools
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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.


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

Problems in Mathematics of KöMaL, January 2017