| Module objective: To introduce the student to elementary Number Theory.
Induction. The division algorithm and the Euclidean algorithm in Z. The fundamental theorem of arithmetic. The integers modulo n. Fermat's Little Theorem, Euler phi function, Euler's generalisation of Fermat's Little Theorem. Wilson's Theorem. Solving Linear Diophantine equations. Solving systems of linear congruences using the Chinese Remainder Theorem. Legendre symbols, quadratic residues, quadratic Law of Reciprocity. Primitive roots. Successive squaring mod n for fast multiplication. Computation using mathematical/statistical software. |