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• ## Re: some questions about algebraic factoring in the field of adjoined square

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• ... In the case of positive d = 3 mod 4, used quadunit(4*d), in Pari-GP, and then take powers of this unit, which has norm = +1. Here is an example with d =
Message 1 of 2 , Jun 21
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> d=4n+2 or d=4n+3
> and the equation of Pell a^2-d*b^2=1
> What is the fastest way to solve the equation of Pell

In the case of positive d = 3 mod 4,
and then take powers of this unit,
which has norm = +1.

Here is an example with d = 139:

for(n=1,100,r*=q;print([n,a=real(r),b=imag(r)]))}

[1, 77563250, 6578829]
[2, 12032115501124999, 1020550716868500]
[3, 1866499965285267079810250, 158314460780301358671171]
...

NB: At n=100, "a" has 819 decimal digits.

David
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