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17 Lectures on Fermat Numbers [2001]

1
Introduction
9
Fundamentals of Number Theory
26
Basic Properties of Fermat Numbers
33
The Most Beautiful Theorems on Fermat Numbers
41
Primality of Fermat Numbers
59
Divisibility of Fermat Numbers
70
Factors of Fermat Numbers
80
Connections of Fermat Numbers with Pascal’s Triangle
94
Miscellaneous Results
104
The Irrationality of the Sum of Some Reciprocals
117
Fermat Primes and a Diophantine Equation
130
Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes
147
Generalizations of Fermat Numbers
158
Open Problems
165
Fermat Number Transform and Other Applications
187
The Proof of Gauss’s Theorem
193
Euclidean Construction of the Regular Heptadecagon
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