pg score/38
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MATH 506 Number Theory – Exam II
Wednesday March 28, 2012
Check that that you have all three pages - note that page two is on the back of page one
1. (14 points) Let a= 233252137, b = 253313519.
(a) The prime factorization of gcd(a, b) = .
(b) The prime factorization of lcm(a, b) = .
(c) If 3e|| 6a2+ 5b3then e= .
(d) If 3f||100! then f= .
2. (18 points) (a) Evaluate τ(700) = .
(b) Evaluate σ(700) = .
(c) What prime factorizations are possible for nif τ(n) = 6?
(d) If pand qare distinct primes then τ(p2q3) = . List the divisors of p2q3(table form is fine).
3. (6 points) Give (with justification) a non-trivial factor of 240 + 1.
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