Math 780 Elementary Number Theory
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Math 780: Elementary Number Theory. (Instructor’s Notes)*. What Is It?:. Elementary Number Theory is the study of numbers, and in particular the study of …
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Math .. Elementary Number Theory
..Instructors Notes
What Is It
.. Elementary Number Theory is the study of numbers.. and in particular the study of
the set of positive integers
.. Does elementary mean easy No
.. Example Consider a positive integer m ..…. and view it as a four digit number
with possible leading digit Suppose all four digits are distinct Let k be the number
obtained by putting the digits of m in increasing order.. and let be the number obtained
by putting the digits in decreasing order Let m.. k Now repeat the process with m..
in place of m Continue What happens How can this be explained
Rational and Irrational Numbers
.. De
ne them
.. Theorem p is irrational..
.. Give typical proof
.. Theorem An irrational number to an irrational power can be rational..
.. Proof Consider p
p…
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