In: Advanced Math
MAT 204 Discrete Structures – Assignment #10
Number theory is the branch of mathematics concerned with the integers. Traditionally, number theory was a pure branch of mathematics – known for its abstract nature rather than its applications. The great English mathematician, G.H. Hardy (1877 – 1947), used number theory as an example of a beautiful, but impractical, branch of mathematics. However, in the late 1900s, number theory became extremely useful in cryptosystems – systems used for secure communications.
Find the following for each pair of integers:
(a) The prime factorization;
(b) The greatest common divisor;
(c) The least common multiple;
(d) Verify that gcd (m, n) * lcm(m, n) = mn.
(i) 315, 825
(ii) 2091, 4807