Authors: Marius Coman
Prime numbers have always fascinated mankind. For mathematicians, they are a kind of “black sheep” of the family of integers by their constant refusal to let themselves to be disciplined, ordered and understood. But we have at hand a powerful tool, insufficiently investigated yet, which can help us in understanding them: Fermat pseudoprimes. Exceptions to Fermat’s “little” Theorem, these numbers seem to be more malleable than primes, more willing to let themselves to be ordered than them, and their depth study will surely shed light on many properties of the primes. I titled the book this way to show how many new and exciting things one can say more about this class of numbers, but, beside the two hundred conjectures (listed in the Part one of this book) and the one hundred and fifty open problems (listed in the Part four of this book), promised in the title, there are many other observations about Fermat pseudoprimes and generic formulas of subsets of Carmichael numbers and Poulet numbers contained in this book. All the articles in this book of collected papers use well-known notions of number theory, with only two exceptions, namely one article in which I defined a new concept, id est “a set of Smarandache-Coman divisors of order k of a composite integer n with m prime factors” and one article in which I have showed several applications of this concept in the study of Fermat pseudoprimes.
Comments: 132 Pages.
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