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

                                     PELL = 17

PELL 17

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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