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Find all integers x,y for a fixed integer a

Source: Austrian Mathematical Olympiad 1997, Part 2, D1, P1

July 4, 2011

number theory proposednumber theory

Problem Statement

Let

a

be a fixed integer. Find all integer solutions

x, y, z

of the system

5x + (a + 2)y + (a + 2)z = a,

(2a + 4)x + (a^2 + 3)y + (2a + 2)z = 3a - 1,

(2a + 4)x + (2a + 2)y + (a^2 + 3)z = a + 1.