Pure Math 340 Midterm Solutions
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1. Let pn be the n-th prime. Ie. p1 = 2, p2 = 3, p3 = 5, . Show that
n
pn 22 for all n.
It is clearly true for n = 1, 2 and 3. Assume that it is not true for all
n
n. Pick n such that it is the minimal value such that

CHAPTER 1
Primes
1.1. Divisibility
Let a, b Z. We say that a divides b or that b is a multiple of a, if b = ma for
some m Z. We, then, also say that b is divisible by a, and that a is a divisor, or
factor, of b.
A shorthand way of writing a divides b, is

PMATH 340 Midterm
Michael Coons
February 12, 2010
Name:
Student Number:
Instructions:
Attempt each problem.
Simple calculators are allowed.
Explain your work carefully, and completely. If you are using a result from class, or
the notes, give an indicat