pg score/32
Name:
MATH 506 Number Theory – Exam I
Wednesday February 15, 2012
Check that that you have all three pages - note that page two is on the back of page one
1. (16 points) (a) Use the Euclidean algorithm to compute gcd(4331,1342) = .
(b) Compute lcm(4331,1342) = .
(c) Write gcd(4331,1342) as a linear combination of 4331 and 1342.
2. (8 points) Show that n6+ 6
7is an integer for all integers n6≡ 0 mod 7.
3. (8 points) Use the definition of divisibility to prove that if a|band b|cthen a2|(b2+ 3bc).
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