## Pythagorean triples of the form (x, y, y+50)

$x \; = \; 10 \,(10 \, n + 1)$
$y \; = \; (10 \, n + 1)^2 \; - \; 25$
$z \; = \; (10 \, n + 1)^2 \; + \; 25$

$x \; = \; 10 \,(10 \, n + 3)$
$y \; = \; (10 \, n + 3)^2 \; - \; 25$
$z \; = \; (10 \, n + 3)^2 \; + \; 25$

$x \; = \; 10 \,(10 \, n + 7)$
$y \; = \; (10 \, n + 7)^2 \; - \; 25$
$z \; = \; (10 \, n + 7)^2 \; + \; 25$

$x \; = \; 10 \,(10 \, n + 9)$
$y \; = \; (10 \, n + 9)^2 \; - \; 25$
$z \; = \; (10 \, n + 9)^2 \; + \; 25$

$x \; = \; 20 \, (5 \, n + 1)$
$y \; = \; 100 \, (n + 1/5)^2 \; - \; 25$
$z \; = \; 100 \, (n + 1/5)^2 \; + \; 25$

$x \; = \; 20 \, (5 \, n + 2)$
$y \; = \; 100 \, (n + 2/5)^2 \; - \; 25$
$z \; = \; 100 \, (n + 2/5)^2 \; + \; 25$

$x \; = \; 20 \, (5 \, n + 3)$
$y \; = \; 100 \, (n + 3/5)^2 \; - \; 25$
$z \; = \; 100 \, (n + 3/5)^2 \; + \; 25$

$x \; = \; 20 (5 \, n + 4)$
$y \; = \; 100 \, (n + 4/5)^2 \; - \; 25$
$z \; = \; 100 \, (n + 4/5)^2 \; + \; 25$

$x \; = \; 50 \, (2 \, n + 1)$
$y \; = \; 25 \, (2 \, n + 1)^2 \; - \; 25$
$z \; = \; 25 \, (2 \, n + 1)^2 \; + \; 25$

$x \; = \; 100 \, n$
$y \; = \; 100 \, n^2 \; - \; 25$
$z \; = \; 100 \, n^2 \; + \; 25$