quadratic residue technique

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• Quadratic reciprocity — The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which shows a remarkable relationship between the solvability of certain quadratic equations modulo different prime moduli.Although it allows us to… …   Wikipedia

• Quadratic sieve — The quadratic sieve algorithm (QS) is a modern integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is… …   Wikipedia

• Lucas–Lehmer test for Mersenne numbers — This article is about the Lucas–Lehmer test (LLT), that only applies to Mersenne numbers. There is also a Lucas Lehmer Riesel test for numbers of the form N=k 2^n 1, with 2^n > k, based on the LLT: see Lucas Lehmer Riesel test. There is also a… …   Wikipedia

• Rabin cryptosystem — The Rabin cryptosystem is an asymmetric cryptographic technique, whose security, like that of RSA, is related to the difficulty of factorization. However the Rabin cryptosystem has the advantage that the problem on which it relies has been proved …   Wikipedia

• Generalized continued fraction — In analysis, a generalized continued fraction is a generalization of regular continued fractions in canonical form in which the partial numerators and the partial denominators can assume arbitrary real or complex values.A generalized continued… …   Wikipedia

• Graphene — is a one atom thick planar sheet of sp2 bonded carbon atoms that are densely packed in a honeycomb crystal lattice. It can be viewed as an atomic scale chicken wire made of carbon atoms and their bonds. The name comes from GRAPHITE + ENE;… …   Wikipedia

• Kloosterman sum — In mathematics, a Kloosterman sum is a particular kind of exponential sum. Let a , b , m be natural numbers. Then :K(a,b;m)=sum {0leq xleq m 1, gcd(x,m)=1 } e^{2pi i (ax+bx^*)/m},Here x* is the inverse of x modulo m . They are named for the Dutch …   Wikipedia

• Cipolla's algorithm — In computational number theory, Cipolla s algorithm is a technique for solving a congruence of the form x2 = n, where , so n is the square of x, and where p is an odd prime. Here denotes the finite field with p elements; . Th …   Wikipedia