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Intro to Abstract Math
Homework 5
Fall 2009
Due September 14
Exercise 13.
Let
x,y
∈
Z
. Prove that if
xy
is odd then
x
and
y
are both odd.
Exercise 14.
Prove that all prime numbers greater than 2 are odd.
Exercise 15.
Show that log
2
(3) is irrational.
Notation:
For
a,b
∈
Z
if
a
divides
b
we write
a

b
.
Deﬁnition:
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Unformatted text preview: An natural number p ≥ 2 is called prime if the only natural numbers that divide p are 1 and p . Theorem: Let a,b ∈ Z and p ∈ N . If p is prime and p  ab then p  a or p  b . Recall: log a ( x ) = y if and only if a y = x ....
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This note was uploaded on 02/29/2012 for the course MATH 3326 taught by Professor Ryandaileda during the Fall '09 term at Trinity University.
 Fall '09
 RyanDaileda
 Prime Numbers

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