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MAT 204 Discrete Structures – Assignment #10 Number theory is the branch of mathematics concerned with...

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MAT 204 Discrete Structures – Assignment #10

Number theory is the branch of mathematics concerned with theintegers. Traditionally, number theory was a pure branch ofmathematics – known for its abstract nature rather than itsapplications. The great English mathematician, G.H. Hardy (1877 –1947), used number theory as an example of a beautiful, butimpractical, branch of mathematics. However, in the late 1900s,number theory became extremely useful in cryptosystems – systemsused 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

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