DETERMINATION OF ALL CLASSES OF POSITIVE
... eliminated immediately by showing that they do not represent some small integer. Forms which pass these tests are scrutinized more carefully and submitted to more powerful number theoretic tests for proving universality. To prove the remaining forms universal it was necessary to use three somewhat d ...
... eliminated immediately by showing that they do not represent some small integer. Forms which pass these tests are scrutinized more carefully and submitted to more powerful number theoretic tests for proving universality. To prove the remaining forms universal it was necessary to use three somewhat d ...
Lecture 7
... the numbers getting too large” or we can calculate a result using standard integer arithmetic throughout and then reduce the result to a modular number at the end; the end result is always the same. Non-prime Moduli If the modulus is not prime, some numbers have inverses and others do not. For examp ...
... the numbers getting too large” or we can calculate a result using standard integer arithmetic throughout and then reduce the result to a modular number at the end; the end result is always the same. Non-prime Moduli If the modulus is not prime, some numbers have inverses and others do not. For examp ...
Discrete Mathematics in the High School Curriculum.
... sa + tn = 1. Therefore sa ≡ 1 (mod n). In this case the equation ax ≡ b (mod n) behaves in the same way as the ordinary equation ax = b over the real numbers: multiply by s ( the inverse of a modulo n), and we find exactly one solution x = sb (mod n). If gcd(a, n) > 1, then the situation is essentia ...
... sa + tn = 1. Therefore sa ≡ 1 (mod n). In this case the equation ax ≡ b (mod n) behaves in the same way as the ordinary equation ax = b over the real numbers: multiply by s ( the inverse of a modulo n), and we find exactly one solution x = sb (mod n). If gcd(a, n) > 1, then the situation is essentia ...