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The Pratt certificate is a primality certificate based on Fermat's little theorem converse. Prior to the work of Pratt (1975), the Lucas-Lehmer test had been regarded purely ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

A pseudoprime is a composite number that passes a test or sequence of tests that fail for most composite numbers. Unfortunately, some authors drop the "composite" ...

An algebraic integer of the form a+bsqrt(D) where D is squarefree forms a quadratic field and is denoted Q(sqrt(D)). If D>0, the field is called a real quadratic field, and ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...

A sequence produced by the instructions "reverse, add to the original, then sort the digits." For example, after 668, the next iteration is given by 668+866=1534, so the next ...

A public-key cryptography algorithm which uses prime factorization as the trapdoor one-way function. Define n=pq (1) for p and q primes. Also define a private key d and a ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

The rank polynomial R(x,y) of a general graph G is the function defined by R(x,y)=sum_(S subset= E(G))x^(r(S))y^(s(S)), (1) where the sum is taken over all subgraphs (i.e., ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...