MathDB

After the schoolday is over, Juku must attend an extra math class. The teacher writes a quadratic equation x^2\plus{} p_1x\plus{}q_1 \equal{} 0 with integer coefficients on the blackboard and Juku has to find its solutions. If they are not both integers, Jukumay go home. If the solutions are integers, then the teacher writes a new equation x^2 \plus{} p_2x \plus{} q_2 \equal{} 0, where

p_2

and

q_2

are the solutions of the previous equation taken in some order, and everything starts all over. Find all possible values for

p_1

and

q_1

such that the teacher can hold Juku at school forever.

Problem Statement