Catalan numbers modulo .
Catalan numbers, the Hankel transform, and Fibonacci numbers.
Catalan without logarithmic forms (after Bugeaud, Hanrot and Mihăilescu)
This is an exposition of the recent work of Bugeaud, Hanrot and Mihăilescu showing that Catalan’s conjecture can be proved without using logarithmic forms and electronic computations.
Catalanova domněnka dokázána
Catalan’s conjecture
The subject of the talk is the recent work of Mihăilescu, who proved that the equation has no solutions in non-zero integers and odd primes . Together with the results of Lebesgue (1850) and Ko Chao (1865) this implies the celebratedconjecture of Catalan (1843): the only solution to in integers and is . Before the work of Mihăilescu the most definitive result on Catalan’s problem was due to Tijdeman (1976), who proved that the solutions of Catalan’s equation are bounded by an absolute...
Catalan's equation has no new solution with either exponent less than 10651.
Catalan's identity and Chebyshev polynomials of the second kind.
Catalan-Zahlen und Wege in einem ganzzahligen Gitter.
Categories of Semigroups with Divisor Theory
Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.
Cauchy multiplication and periodic functions (mod r).
We analise periodic functions (mod r), keeping Cauchy multiplication as the basic tool, and pay particular attention to even functions (mod r) having the property f(n) = f((n,r)) for all n. We provide some new aspects into the Hilbert space structure of even functions (mod r) and make use of linera transformations to interpret the known number-theoretic formulae involving solutions of congruences.
Cayley orders
Cell decomposition for two dimensional local fields
Census algorithms for chinese remainder pseudorank
We investigate the density and distribution behaviors of the chinese remainder representation pseudorank. We give a very strong approximation to density, and derive two efficient algorithms to carry out an exact count (census) of the bad pseudorank integers. One of these algorithms has been implemented, giving results in excellent agreement with our density analysis out to -bit integers.
Census algorithms for chinese remainder pseudorank
We investigate the density and distribution behaviors of the chinese remainder representation pseudorank. We give a very strong approximation to density, and derive two efficient algorithms to carry out an exact count (census) of the bad pseudorank integers. One of these algorithms has been implemented, giving results in excellent agreement with our density analysis out to 5189-bit integers.
Central and genus class fields and the Hasse norm theorem
Central binomial sums, multiple Clausen values, and zeta values.
Central Characters for Smooth Irreducible Modular Representations of
Central extensions and reciprocity laws
Certain classes of arithmetic functions and the operation of additive convolution.