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Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
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Primality test similar to the AKS test
Let us define polynomials $P_n^{(a)}(x)$ as follows :
$P_n^{(a)}(x)=\left(\frac{1}{2}\right)\cdot\left(\left(x-\sqrt{x^2+a}\right)^n+\left(x+\sqrt{x^2+a}\right)^n\right)$
We can define these polynom …
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What is the most efficient algorithm for calculating $\Phi_q(b) \operatorname{mod} N$?
paper mentioned above) for calculating $\Phi_{mp}(x) \operatorname{mod} M$ , where $m$ is an odd squarefree integer , $p$ is a prime not dividing $m$ and $M$ is a prime , but I am not sure if these two algorithms …