منابع مشابه
On Dickson's Theorem Concerning Odd Perfect Numbers
A 1913 theorem of Dickson asserts that for each fixed natural number k, there are only finitely many odd perfect numbers N with at most k distinct prime factors. We show that the number of such N is bounded by 4k 2 .
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We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd Chern classes for cocycles in odd K-theory. Moreover we discover that in odd dimensions, the fundamental group of manifolds plays an important role in the rigidity.
متن کاملA Short Proof of the Odd-Girth Theorem
Recently, it has been shown that a connected graph Γ with d+1 distinct eigenvalues and odd-girth 2d + 1 is distance-regular. The proof of this result was based on the spectral excess theorem. In this note we present an alternative and more direct proof which does not rely on the spectral excess theorem, but on a known characterization of distance-regular graphs in terms of the predistance polyn...
متن کاملA Machine-Checked Proof of the Odd Order Theorem
This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a comprehensive set of reusable libraries o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0270757-2