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Results tagged with nt.number-theory
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user 402326
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Computing Lucas sequence for large n
I've been trying to write a test function for Fibonacci pseudo-primes with large $n$. Fibonacci pseudoprimes are composite numbers such that $V_n(P,Q) \equiv P \mod n$ for $P>0$ and $Q =\pm 1$, with $ …
- 11
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Computing Lucas sequence for large n
Following Emil remark, I used other relations to obtain a $O(\log n)$ algorithm:
$\begin{cases}U_{2n}=U_nV_n\\
V_{2n}=V_n^2-2Q^n\\
U_{2n+1} = U_{n+1}V_n - Q^n\\
V_{2n+1} = V_{n+1}V_n -PQ^n\end{cases}$ …
- 11