Pell's Equation

  • Thread starter wii
  • Start date
  • #1
wii
12
0
I want to solve this equation

[tex]x^2 - 18 y^2 = 12[/tex]

Any suggestion?

I thought , we have to find [itex]\sqrt 18[/itex]and then find [tex]x/y[/tex]

BUT I was confused and then stopped solving
 

Answers and Replies

  • #2
2,967
5
This equation has 2 unknowns. If you don't specify what set x and y are elements of, for example integer, it has an infinite set of solutions that can be represented parametrically as:

[tex]
\begin{array}{l}
x = \pm 2 \sqrt{3} \, \cosh{t} \\

y = \frac{2 \sqrt{3}}{3} \, \sinh{t}
\end{array}
[/tex]
 
Last edited:
  • #3
wii
12
0
Sorry,
Both x & y are integers.
 
  • #4
273
0
You might get more help if you posted this in the Number Theory section...
 
  • #5
2,967
5
There is no solution.
 

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