Puzzle of the Week #225 - Six Integers

x^2 = a^2 + 4b + 1

y^2 = b^2 + 4c + 1

z^2 = c^2 + 4a + 1

a, b, c, x, y, z are all positive integers

a > b > c

x > y > z

What are the values of the six integers?

 

(There is a really neat algebraic trick you can use here. First see if you can calculate x in terms of a).