Question 64
In a math period, the teacher asks pupils to solve quadratic equations of the form $x^2 + px + q = 0$ where $p$ and $q$ are some integers. The teacher obtains every new equation by either increasing by 1 or decreasing by 1 the value of either $p$ or $q$ in the equation just solved. In the initial equation, $p = 2020$ and $q = 2010$, whereas in the last equation, $p = 2010$ and $q = 2020$. Is it definitely true that both solutions of at least one equation solved during the period are integers?