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The Chinese Remainder Theorem and Multiplicativity
We presented \(\mathbb {Z}/q\mathbb {Z}\) in...
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Identification of proteins by the use of Chinese remainder theorem codes over finite commutative rings
In recent works, error-correcting codes have been applied for modeling the reliability in the transmission of genetic information, wherein DNA and...
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The Chinese Middle Ages
Just at the time that the civilizations of Egypt and Babylon were develo** in the borderlands of the three continents of Asia, Africa, and Europe,...
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The Chebotarev Density Theorem
The major connection between the theory of finite fields and the arithmetic of number fields and function fields is the Chebotarev density theorem....
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Applications of the Chinese Remainder Theorem
It applies to coprime ideals in a not necessarily commutative ring.
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On the Garden of Eden theorem for ℬ-free subshifts
We prove that on ℬ-free subshifts, with ℬ satisfying the Erdős condition, all cellular automata are determined by monotone sliding block codes. In...
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On some congruences of sums of powers and Wolstenholme’s theorem for generalized harmonic numbers
In this paper, we first attempt to study sums of powers and to obtain some divisibility properties of the Stirling numbers of the first kind based on...
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Influence of the Baer–Kaplansky Theorem on the Development of the Theory of Groups, Rings, and Modules
The review presents an analysis of results of the Abelian group theory, as well as rings and modules, which concern the definability of algebraic...
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Some q-supercongruences from squares of basic hypergeometric series
Inspired by the recent work of El Bachraoui and Guo-Li, we establish several q -supercongruences on the truncated forms of squares of basic...
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Modular forms and an explicit Chebotarev variant of the Brun–Titchmarsh theorem
We prove an explicit Chebotarev variant of the Brun–Titchmarsh theorem. This leads to explicit versions of the best known unconditional upper bounds...
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Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
In this paper, three parametric q -supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the...
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The Intimate Interplay Between Experimentation and Deduction: Some Classroom Implications
We understand experimental mathematics as the systematic experimental investigation of concrete examples of a mathematical structure in the search...
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The Modularity Theorem
This chapter presents the quadratic reciprocity law and the modularity of Kronecker characters and applies the results to Terjanian’s theorem on the...
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Polynomial Schur’s Theorem
We resolve the Ramsey problem for { x,y,z : x + y = p ( z )} for all polynomials p over ℤ. In particular, we characterise all polynomials that are...
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Approximation Algorithms for Solving the k-Chinese Postman Problem Under Interdiction Budget Constraints
In this paper, we address the k -Chinese postman problem under interdiction budget constraints (the k -CPIBC problem, for short), which is a further...
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The Intimate Interplay Between Experimentation and Deduction: Some Classroom Implications
We understand experimental mathematics as the systematic experimental investigation of concrete examples of a mathematical structure in the search...
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q-Supercongruences from squares of basic hypergeometric series
We give some new q -supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic...