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on highly composite and similar numbers
on highly composite and similar numbers

INTEGRATING MORPHISMS OF LIE 2-ALGEBRAS 1. Introduction In
INTEGRATING MORPHISMS OF LIE 2-ALGEBRAS 1. Introduction In

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... the use of objects representing the power set construction that play such a central rôle in the Lawvere-Tierney theory. On the other hand, it is possible to adjoin quotients of equivalence relations at the level of type theory (known as setoids in the type theory literature) which together with the ...
Farmat`s Last Theorem
Farmat`s Last Theorem

Secondary 2 textbook
Secondary 2 textbook

Chapter 9 Lie Groups, Lie Algebras and the Exponential Map
Chapter 9 Lie Groups, Lie Algebras and the Exponential Map

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Settling a Question about Pythagorean Triples

IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN:2319-765X.
IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN:2319-765X.

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Basic Algebra Skills

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... H-fixed points and the G-fixed points for any G-equivariant spectrum, and morally, we should continue to think of the transfer as “summing over the Weyl group”. The source of the transfer has been a perpetual source of confusion, and the language of an F-commutative monoid can be used to describe wh ...
Asymptotic formulæ for the distribution of integers of various types∗
Asymptotic formulæ for the distribution of integers of various types∗

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Folding and unfolding in periodic difference equations

... of O+ (x0 ) = (xn ), which can be denoted by ord[f0 ,...,fp−1 ] (x0 ). By P([f0 , ..., fp−1 ]) and Per([f0 , . . . , fp−1 ]) we denote the sets of periodic points and periods of [f0 , . . . , fp−1 ], respectively. Note that in discrete autonomous systems if x0 ∈ P([f0 ]), then xn ∈ P([f0 ]) for all ...
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Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.
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