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17 Lectures on Fermat Numbers [2001]
- 1
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Introduction
- 9
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Fundamentals of Number Theory
- 26
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Basic Properties of Fermat Numbers
- 33
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The Most Beautiful Theorems on Fermat Numbers
- 41
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Primality of Fermat Numbers
- 59
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Divisibility of Fermat Numbers
- 70
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Factors of Fermat Numbers
- 80
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Connections of Fermat Numbers with Pascal’s Triangle
- 94
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Miscellaneous Results
- 104
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The Irrationality of the Sum of Some Reciprocals
- 117
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Fermat Primes and a Diophantine Equation
- 130
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Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes
- 147
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Generalizations of Fermat Numbers
- 158
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Open Problems
- 165
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Fermat Number Transform and Other Applications
- 187
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The Proof of Gauss’s Theorem
- 193
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Euclidean Construction of the Regular Heptadecagon