Problem B KöMaL Math Contest 2019 | Junior Math Olympiad Training
Consider the quadratic function f(x)=x² + bx + c defined on the set of real numbers. Given that the zeros of f are some distinct prime numbers p and q, and f(p−q)=6pq, determine the primes p and q and determine the function f.
What is KöMaL?
It was more than a hundred years ago that Dániel Arany, a high school teacher from the city of Győr, decided to found a mathematical journal for high school students. His goal was "to give a wealth of examples to students and teachers". The journal's first edition appeared on January 1, 1894.
The foundation of the journal had close connections with the boom in scientific life at the turn of the century. The Mathematical and Physical Society was founded in 1891, and in the autumn of 1894 the first Eötvös Competition in mathematics was organised for students that just graduated from high school.
From that time several generations of mathematicians and scientists developed their problem-solving skills through KöMaL. The best solutions with the names of the 14-18 year-old authors are printed in the periodical.
At present, the journal is published by the MATFUND Hungarian High School Mathematics and Physics Foundation, the János Bolyai Mathematical Society and the Roland Eötvös Physical Society with the financial support of the Ministry of Education and Culture in 3500 copies.
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