2539762
Exam 3
- Definition
- order of an integer modulo p
- Perfect Numbers
- Mersenne primes
- Fermat primes
- Fibonacci sequence
- Pythagorean
triples, and
primitive
Pythagorean
triples.
- order of an integer modulo p
- Prove
- Theorem 8.1
- The Lemma on pg. 221
regarding when a^k -1 is
prime.
- Theorem 14.2; will be
given the identity (a)
on page 289
- Converse of
Theorem 12.1 (top
of page 249)
- Theorem 8.1
- Understand
- The cyclic nature
of the list a, a^2,
a^3, ... as well as
the relationship
between the
repeats on the list
and the order of a
modulo p
- The cyclic nature
of the list a, a^2,
a^3, ... as well as
the relationship
between the
repeats on the list
and the order of a
modulo p
- Know
- Theorem 8.3: The
statement and the
idea of the proof of
the formula o(a^i)
- When primitive roots
exist, how many are
there?
- The idea in
the proof of
Lagrange's
Theorem. In
particular, if
ab=0 (mod p),
b=0 (mod p).
- The statement
of Theorem 8.6
(whose corollary
gives the
existence of
primitive roots
for primes.)
- The statement
of Theorem 11.1
regarding the
existence of
perfect
numbers. (Prove
the 'if'
direction.)
- Statement of
Theorem
14.3
- Theorem 8.3: The
statement and the
idea of the proof of
the formula o(a^i)
- Be able to
- Given an element of
a certain order (mod
p), use thm. 8.3 to
produce elements of
prescribed orders
(example 8.1)
- Problems in
homework
regarding
perfect
numbers.
- Given an element of
a certain order (mod
p), use thm. 8.3 to
produce elements of
prescribed orders
(example 8.1)
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