Pocklington's Algorithm, Kartoniert / Broschiert

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pocklington's algorithm is a technique for solving a congruence of the form x^2 equiv a pmod p, , where x and a are integers and a is a quadratic residue. The algorithm is one of the first efficient methods to solve such a congruence. It was described by H. C. Pocklington in 1917. (Note: all equiv are taken to mean (mod p), unless indicated otherwise.) In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square (mod n); i. e., if there exists an integer x such that: {x^2}equiv {q} pmod{n}. Otherwise, q is called a quadratic nonresidue (mod n). Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.