## PPT & x^2 – 2*y^2 = 17

Older post :     PPT & x^2 – 2*y^2 = 7

$x^2 \; - \; 2 \, y^2 \; = \; 17$

the sum p of its two legs can be expressed as the Pell-like equation,

$(m^2-n^2) \; + \; (2 \, m \, n) \; = \; (m+n)^2 \; - \; 2 n^2 \; = \; x^2 \; - \; 2 \, y^2 \; = \; p$        Eq #1

For example,     $p \; = \; 17$

$x^2 \; - \; 2 \, y^2 \; = \; 17$

$a \; = \; | \,m^2-n^2 \,|$ ,    $b \; = \; 2 \, m \, n$ ,    $c \; = \; m^2+n^2$ ,

$a^2 \; + \; b^2 \; = \; c^2$,    (a, b, c)   is a Primitive Pythagorean triple.

$5^2 \; - \; 2\times 2^2 \; = \; 17$
$7^2 \; - \; 2\times 4^2 \; = \; 17$
$23^2 \; - \; 2\times 16^2 \; = \; 17$
$37^2 \; - \; 2\times 26^2 \; = \; 17$
$133^2 \; - \; 2\times 94^2 \; = \; 17$
$215^2 \; - \; 2\times 152^2 \; = \; 17$
$775^2 \; - \; 2\times 548^2 \; = \; 17$
$1253^2 \; - \; 2\times 886^2 \; = \; 17$
$4517^2 \; - \; 2\times 3194^2 \; = \; 17$
$7303^2 \; - \; 2\times 5164^2 \; = \; 17$
$26327^2 \; - \; 2\times 18616^2 \; = \; 17$
$42565^2 \; - \; 2\times 30098^2 \; = \; 17$
$153445^2 \; - \; 2\times 108502^2 \; = \; 17$
$248087^2 \; - \; 2\times 175424^2 \; = \; 17$
$894343^2 \; - \; 2\times 632396^2 \; = \; 17$
$1445957^2 \; - \; 2\times 1022446^2 \; = \; 17$
$5212613^2 \; - \; 2\times 3685874^2 \; = \; 17$
$8427655^2 \; - \; 2\times 5959252^2 \; = \; 17$
$30381335^2 \; - \; 2\times 21482848^2 \; = \; 17$
$49119973^2 \; - \; 2\times 34733066^2 \; = \; 17$
$177075397^2 \; - \; 2\times 125211214^2 \; = \; 17$