New answers tagged pell-type-equations
-1
votes
Rational solutions of Pell's equation
The difference equation given by initial conditions
$a_0=0$, $b_0=1$ and the recursion:
$a_{n+1}=A\times a_n+B\times b_n$
and
$b_{n+1}=N\times B\times a_n+A\times b_n$
Gives solutions to:
$(b_n)^2-N\...
0
votes
Find all primes $p$ and $q$ such that $p^2-2q^2=1.$
One more approach (just for exercising).
We use the knowledge that $1=3^2-2 \cdot 2^2$ and rewrite the initial formula as
$$ p^2 - 2q^2 = 3^2-2 \cdot 2^2 \tag 1$$
and then
$$ p^2 - 3^2 = 2(q^2-2^2) \...
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