Pell equation : x^2 – 113*y^2 = ± 1

 

x^2 \; - \; 113 \, y^2 \; = \; -1
 
Here are the first few solutions:
 

x \; = \; 776
y \; = \; 73

x \; = \; 1869156632
y \; = \; 175835465

x \; = \; 4502248794437416
y \; = \; 423535939558217

x \; = \; 10844593684652301387064
y \; = \; 1020173558829338801737

x \; = \; 26121437875779604016034941768
y \; = \; 2457298172193157811837164105

 
 

x^2 \; - \; 113 \, y^2 \; = \; +1
 

x \; = \; 1204353
y \; = \; 113296

x \; = \; 2900932297217
y \; = \; 272896754976

x \; = \; 6987493029899166849
y \; = \; 657328051091107760

x \; = \; 16830816386073401651890177
y \; = \; 1583310020631184911403584

x \; = \; 40540488414026331506287881514113
y \; = \; 3813728346553801555156190094544

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

2 Responses to Pell equation : x^2 – 113*y^2 = ± 1

  1. paul says:

    These two are interesting using x^2 – n y^2 = 1

    9801^2 – 725 * 364^2 = 1.
    458^2 – 209763 *1^2 = 1

    x, y and n are 0 – 9 pan digital.

    and this one

    30769208^2 – 5651487*12943^2 = 1

    is 2 lots of 0 – 9 digits for x, y, and n

    Paul.

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