Quiz1a-b-solnkey - arithmetic (think before you answer)?...

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CSE 565 Q1. Find the Multiplicative Inverse of (a) 4 mod 5, (b) 6 mod 7 Ans: (a) 4 (b) 6 Q2. Evaluate (a) GCD (60, -24), (b) GCD (1,0) Ans: (a) 12 (b) 1 Q3. Is 3 a primitive root modulo 14? Why/Why not? Ans: Yes Q1. Find the Multiplicative Inverse of 24140 mod 40902. Ans: Since gcd (24140, 40902) <> 1, no inverse exists. Q2. Evaluate (a) GCD (60, 24), (b) GCD (60,-24). In one or two sentences explain when is the negative sign significant/insignificant in modulo
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Unformatted text preview: arithmetic (think before you answer)? Ans: (a) 12 (b) 12 Sign matters in modulo arithmetic. By definition, if a is an integer (+ or -) and n is a +ve integer, then we say b = (a mod n), which is the remainder when a is divided by n. The property that a b (mod n) if n | (a-b) gives different values for b depending upon whether a is positive or negative. Q3. Is 5 a primitive root modulo 14? Why/Why not? Ans: Yes...
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This note was uploaded on 10/12/2010 for the course CSE 565 taught by Professor Shambhu during the Fall '09 term at SUNY Buffalo.

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