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Unformatted text preview: (a) a + c b + d (mod m ) (b) ac bd (mod m ) Note: If a = q a m + r a and b = q b m + r b where r a < m and r b < m it is possible that r a + r b m . 3. Construct the multiplication table for arithmetic mod 7. 4. (Extended Euclidean Algorithm) What is multiplicative inverse of 400 mod 997? 5. (a) Prove for relatively prime a and b that if a divides bc , then a divides c . Hint : First show that there exist s and t such that sac + tbc = c and then argue that a divides c . (b) Give counter example when a and b are not relatively prime. 1...
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This note was uploaded on 11/11/2011 for the course CS 2800 at Cornell University (Engineering School).