These 7 exercises are for review - do not turn them in.
Section 0.1, exercise 4
Section 0.1, exercise 6
Section 0.2, exercises 1-5
Section 0.2, exercise 10 (This one is more challenging - here are
two
possible approaches: (1) Use
the fact that the Euler φ-function is multiplicative. You should be
able to prove that φ (n) ≥ (1/2) √ n without too much difficulty, or
(2) show first that for any fixed positive integer N there are only
finitely many primes p that could divide any integer k with φ(k) =
N, then consider how large a power of any prime could divide k.)
Section 0.2, exercise 11
Section 0.3, exercises 3-9
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