I found integers

h1, h2, h3,h4 such that

h1 + h2 + h3 + h4 = z

and

h1 * h4 - h2 * h3 = 0.

Then I expected that x = gcd(h1,h2) + gcd(h3,h4) would divided z.

Indeed, x does divide z.

x seems to always be equal to 1.

I haven't yet found a way to generate a set h1,h2,h3,h4

such that all of them are positive,

and

h1 + h2 + h3 + h4 = z,

and

h1 h4 - h2 h3 = 0.

Kermit