Related papers: Proofs of some Conjectures from the OEIS
We provide the results of pattern recognition experiments on mathematical expressions. We give a few examples of conjectured results. None of which was thoroughly checked for novelty. We did not attempt to prove all the relations found and…
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
We prove some symmetric $q$-congruences.
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion…
We give a more strong heuristic justification of our conjecture on the excess of the odious primes.
In this note we present a collection of attempts of some researchers to prove or disprove whether the Zeraoulia sequences convergent. Even nowdays convergence of Zeraoulia sequences still open.
In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.
In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.
In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
In this paper we consider the remaining cases of Hebey-Vaugon conjecture.
We use the automatic theorem prover Walnut to resolve various open problems from the OEIS and beyond. Specifically, we clarify the structure of sequence A260311, which concerns runs of sums of upper Wythoff numbers. We extend a result of…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.
We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.
We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.
We prove that five ways to define entry A086377 in the On-Line Encyclopedia of Integer Sequences do lead to the same integer sequence.