Download Elementary Number Theory

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Preface
This collection of notes summarizes the first half of the Math 175 course at the University of
Chicago in the Fall 2015 quarter. Written very hastily, it has yet to be proofread carefully. All
mistakes are attributable to the author, not to the instructor. The names we give to mathematical
objects and theorems may differ from those in [JJ].
The section numbers roughly correspond to weeks of the quarter. Throughout, we use the
following conventions:
N = {1, 2, 3, . . .}, the set of natural numbers
Z = {0, ±1, ±2, . . .}, the set of integers
Q = {a/b : a, b ∈ Z and b 6= 0}, the set of rational numbers
R = the set of real numbers
This course is about the algebraic relationships that exist between integers, or more poetically,
the patterns and symmetries hidden within Z and Q. To students: Please, do not feel as though
these notes can only be read front-to-back. They were written to be a “user’s manual,” not a
narrative!
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