How To Factor P times Q From One Square Root Of -1

摘要

#$%^&*AU2016100469A420160526.pdf#####How To Factor P * Q From One Square Root Of -1 Paul C. Bingham Cheffers 17 December 2015 1 Abstract Abstract The paper shows two methods of factoring two primes, P * Q, with knowledge of one of the Eg mod p * q. and some further operations described in the paper. The first method shows that, for 1 mod 4 semiprime modula that 2 * -12 mod p * q ±(VI + 1)2 mod p * q, and that taking the modular square root of this sum (or the natural square root if 2 * V12 mod p * q is a natural square) will lead to an equation that easily factors either p or q from p * q. A Mathematica procedure is then shown, with output, that shows that out of 245,000 possible p * q modula that 26 have 2 * 12 mod p * q as a natural square. The second method shows that a modular number, X mod p * q, expressed in modular complex notation, a + b * El mod p * q = X has a modular complex conjugate a - b * Eg mod p * q = X, and that the four answers of each of two modular quadratic equations, (x+n)2 mod p * q = X, and (x+n)2 mod p * q Xcc can be combined together to solve for P and Q in the field of P * Q. 1