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| viXra.org > Number Theory > 2510 |
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[8] viXra:2510.0154 [pdf] submitted on 2025-10-31 16:30:15
Authors: Fian Qnoz
Comments: 12 Pages. 37 figures.
The exploration of incomplete magic square of squares, whose being fully working magic square with less than 9 square entries, leads to the extensive use of Brahmagupta-Fibonacci identity. By only taking account of primitive (irreducible) entries, the umbrella term Brahmagupta’s Abacial Slice of Irreducible Calamari (BASIC) magical marine square was adopted. Interesting varieties ranging from congruent elliptic curves up to the affine variety A6 along with the K3 surface of degree 8 were encountered when one considers the birational model of Magicmare.
Category: Number Theory
[7] viXra:2510.0135 [pdf] replaced on 2025-12-12 01:08:37
Authors: Zihang Chen
Comments: 10 Pages.
This paper will start with the derivation of the Euler-Maclaurin formula with singularities, compensate for the series divergence problem of its fitting the zeta function by adding a compensation factor ε, perform analytic continuation on the expanded series, analyze the distribution of its trivial zeros through the laws of Bernoulli numbers, and then construct functions and combine the properties of the gamma function to solve the distribution law of non-trivial zeros.
Category: Number Theory
[6] viXra:2510.0129 [pdf] submitted on 2025-10-26 23:04:55
Authors: Pravin Kumar Mishra
Comments: 10 Pages. (Note by viXra Admin: Please cite listed scientific reference)
This paper presents a series of theorems and corollaries in two sections. The 2nd section outlines a method for verifying the existence of prime numbers within specific intervals. Postulates 1 and 2 establish a methodology to verify the existence of primes in the specific intervals shown in Theorem 1 and its corollary and Theorem 2. The 3rd section outlines a prime indicator function that generates all primes sequentially. The construction of this indicator begins from Theorem 3, and Theorem 4 provides insights on the sum of all odd composite numbers, and its corollary produces a prime indicator supported by an Illustration of a few first numbers. This work provides new insights into how to use elementary principles and methods.
Category: Number Theory
[5] viXra:2510.0127 [pdf] submitted on 2025-10-26 22:51:54
Authors: Jean-Yves Boulay
Comments: 47 Pages.
Grounded in a novel mathematical framework, this study partitions the set of whole numbers (ℕ0) into four distinct hierarchical classes. A key innovation is the definition of Ultimate Numbers—the union of the prime numbers with zero and one—which resolves classic conceptual limitations. Three further subsets, representing increasing degrees of numerical complexity, are subsequently defined by the initial distinction between ultimate and non-ultimate numbers within ℕ0. The structural interaction among these four classes yields unique arithmetic arrangements in their initial distribution, most notably revealing an exact and recurring 3:2 ratio.
Category: Number Theory
[4] viXra:2510.0061 [pdf] submitted on 2025-10-13 20:19:05
Authors: Chandhru Srinivasan
Comments: 11 Pages. (Note by viXra Admin: Author name is required in the article; please submit article written with AI assistance to ai.viXra.org)
I report an empirical derived and theoretically motivated analysis of modular patterns in composite integers, with a focus on semiprimes. For any odd semiprime N(possibly all N ∈ ℤ), the results indicate the existence of N-1congruences of the form p+q≡r(modm), where p and q are factors of N, m∈{2,u2026,N-1} as 1 and N are trivial and always N ≡0 mod(1 or N) , and each residue r belongs to a restricted, well-structured subset R_m. Empirical experiments suggest that these residue constraints are non-random, deterministic and encodes all the necessary information about the factor pair (p,q). I formalize this observation as a conjecture and provide preliminary reasoning for its generality. These results point toward a potentially deterministic structure in the modular representation of factor sums, and potentially speedup the factorisation of any N and offering a new perspective on the arithmetic properties of semiprimes and composite numbers. I invite further mathematical verification and formalization.
Category: Number Theory
[3] viXra:2510.0052 [pdf] replaced on 2025-11-15 03:41:26
Authors: Hashem Sazegar
Comments: 7 Pages.
Oppermann’s conjecture states that for every positive integer n, there exists at least one prime number between n 2 and n 2 + n. Priorto this, Legendre had conjectured that there is always at least one prime number between n2 and (n + 1)2 . In this paper, we not onlyclaim to prove Oppermann’s conjecture but also propose a smaller interval, asserting that there exists at least one prime between n 2 andn 2 + n/2.
Category: Number Theory
[2] viXra:2510.0051 [pdf] submitted on 2025-10-09 20:57:18
Authors: Theophilus Agama
Comments: 10 Pages. (Note by viXra Admin: Frequent/incessant submissions of highly speculative/abstract articles will not be accepted)
We prove an extension of the lower bound due to Schonhage on addition chains.
Category: Number Theory
[1] viXra:2510.0022 [pdf] submitted on 2025-10-05 17:27:40
Authors: Islem Ghaffor
Comments: 1 Page.
In this paper we prove Collatz conjecture by giving an equivalent formulation of the shortcut Collatz sequence.
Category: Number Theory
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