Unformatted text preview: (a) a + c â‰¡ b + d (mod m ) (b) ac â‰¡ 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 â‰¥ 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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 '07
 SELMAN
 Number Theory, Prime number, Greatest common divisor, Euclidean algorithm, Prof. Hopcroft, (mod m)

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