Find all numbers a such that the solutions to x^{2} + ax + 1996 = 0 and y^{2} + 1996y + a = 0 are all integers. Source: V. Protasov, Quantum, July/August 1997 © Copyright 1997 Stan Wagon. Reproduced with permission.

Find all numbers a such that the solutions to x^{2} + ax + 1996 = 0 and y^{2} + 1996y + a = 0 are all integers.

Source: V. Protasov, Quantum, July/August 1997

© Copyright 1997 Stan Wagon. Reproduced with permission.