MAD 4301 Midterm: MAS4301 F05 Test 1
Document Summary
Complete the following de nitions. (a) we say that a divides b if . (b) the greatest common divisor of a and b is . (2) (5 pts. ) Give without proof the statement of bezout"s identity. (3) (20 pts. ) No proofs required. (a) ve prime numbers (b) ve composite numbers (c) two numbers that are relatively prime (d) two numbers a and b such that (a, b) = 15 (4) (10 pts. ) State and prove euclid"s lemma. (7) (15 pts. ) Prove using bezout"s identity: if (a, b) = 1 and a|c and b|c, then ab|c. (8) (15 pts. ) Prove using mathematical induction: for all n 1,
