Pandigital | Pell equation : x^2 – k*y^2 = 1

 
Paul found :
 

9801^2 \; - \; 725\times 364^2 \; = \; 1

458^2 \; - \; 209763\times 1^2 \; = \; 1

728^2 \; - \; 6543\times 9^2 \; = \; 1

 
30769208^2 \; - \; 5651487\times 12943^2 \; = \; 1

21543049^2 \; - \; 6893776\times 8205^2 \; = \; 1

 
 

Now, can you find a pandigital solution to    x^2 \; - \; k \, y^2 \; = \; m

the digits of the combined integers (x, k, y, m) contain all digits from 0 to 9 (or 1 to 9)

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

3 Responses to Pandigital | Pell equation : x^2 – k*y^2 = 1

  1. paul says:

    Up to now I can only find a 1-9 solution

    728^2 – 6543 * 9^2 = 1
    P.

  2. paul says:

    Here is a 2 lots 0 – 9 pandigital

    21543049^2 – 6893776 * 8205^2 = 1

    P

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