Results 11 to 20 of about 654 (59)
Proof of the Collatz Conjecture
Theoretical Mathematics & Applications, 2023 The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers ...
Bülent Sukuşu
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Cryptographic Algorithm Based on Prime Assignment
International Journal for Research in Applied Science and Engineering Technology, 2022 : Cryptography is a concept of protecting information and conversations which are transmitted through a public source, so that the send and receiver only read and process it.
M. Mahalakshmi
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Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions
Journal of Inequalities and Applications, 2013 In this paper, we study the convolution sums involving restricted divisor functions, their generalizations, their relations to Bernoulli numbers, and some interesting applications.MSC: 11B68, 11A25, 11A67, 11Y70, 33E99.
Daeyeoul Kim +2 more
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9
Open Mathematics, 2017 The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
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THE NUMBER OF INTEGRAL SOLUTIONS TO AN EQUATION INVOLVING SUMS OF RADICALS
Acta Universitatis Apulensis, 2019 In this short note, we present a Galois-theoretic proof for the following result. Given an integer k ≥ 2 and fixed positive integers n1, . . . , nk, the number of solutions (x1, . . . , xk, y) ∈ (Z≥0) to the equation (1) is finite.
D. Andrica, George C. Ţurcaş
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On the sum of digits of the factorial [PDF]
, 2014 Let b > 1 be an integer and denote by s_b(m) the sum of the digits of the positive integer m when is written in base b. We prove that s_b(n!) > C_b log n log log log n for each integer n > e, where C_b is a positive constant depending only on b.
Sanna, Carlo
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Eisenstein series and their applications to some arithmetic identities and congruences
Advances in Differential Equations, 2013 Utilizing the theory of elliptic curves over ℂ to the normalized lattice Λτ, its connection to the Weierstrass ℘-functions and to the Eisenstein series E4(τ) and E6(τ), we establish some arithmetic identities involving certain arithmetic functions and ...
Daeyeoul Kim +2 more
semanticscholar +2 more sources
, 2017 In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and ...
Feng Qi (祁锋) +2 more
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Generalizations of the Bell Numbers and Polynomials and Their Properties
, 2017 In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of ...
Feng Qi (祁锋) +3 more
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