HW1, due Wednesday September 7

Exercises from MNT chapter 1, pages 14-16

  • MNT, 1.
  • MNT, 15,
  • MNT, 16
  • MNT, 30

 

  • The function pi(x) counting the number of primes up to x is called PrimePi in WolframAlpha.  Use WolframAlpha or other means to calculate pi(x)/(x / ln x), for x = 10^k, for k=2,3,4,5,6.  Does it seem that the limit might approach 1, as predicted by the prime number theorem?
  • The ring of Gaussian integers is a Euclidean domain.  Show directly that the ring is an integral domain.  Apply a division algorithm to divide 3+4i by 1+i and work out its remainder.
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