Related papers: Probable Counterexamples of the ABC Conjecture
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
Computer-based tests with randomly generated questions allow a large number of different tests to be generated. Given a fixed number of alternatives for each question, the number of tests that need to be generated before all possible…
In eXplainable Artificial Intelligence (XAI), several counterfactual explainers have been proposed, each focusing on some desirable properties of counterfactual instances: minimality, actionability, stability, diversity, plausibility,…
In this note we present a construction of an infinite family of diagonal quintic threefolds defined over $\Q$ each containing infinitely many rational points. As an application, we prove that there are infinitely many quadruples $B=(B_{0},…
The Collatz and $abc$ conjectures, both well known and thoroughly studied, appear to be largely unrelated at first sight. We show that assuming the $abc$ conjecture true is helpful to improve the lower bound of integers initiating a…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
In the present paper I shall clarify the Babylonian method by which many large tables of reciprocals could be constructed.
Ellenberg proved that the abc conjecture would follow if this conjecture were known for sums $a+b=c$ such that $D\mid abc$ for some integer~$D$. Mochizuki proved a theorem with an opposite restriction, that the full abc conjecture would…
We present a formal measure of argument strength, which combines the ideas that conclusions of strong arguments are (i) highly probable and (ii) their uncertainty is relatively precise. Likewise, arguments are weak when their conclusion…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
We discuss conjectures related to the following two conjectures: (1) for each complex numbers x_1,...,x_n there exist rationals y_1,...,y_n \in [-2^{n-1},2^{n-1}] such that \forall i \in {1,...,n} (x_i=1 \Rightarrow y_i=1) \forall i,j,k \in…
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
An elaboration of Dempster's method of constructing belief functions suggests a broadly applicable strategy for constructing lower probabilities under a variety of evidentiary constraints.
We study simple superfaithful and superconnected quandles and we found counterexamples to a conjecture suggested by computational data. We provide also examples of superconnected quandles built using group theoretical results and…
We produce an infinite family of transcendental numbers which, when raised to their own power, become rational. We extend the method, to investigate positive rational solutions to the equation $x^x = \alpha$, where $\alpha$ is a fixed…
The literature for count modeling provides useful tools to conduct causal inference when outcomes take non-negative integer values. Applied to the potential outcomes framework, we link the Bayesian causal inference literature to statistical…
We prove some constructive results that on first and maybe even on second glance seem impossible.
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
In this paper, the concept of possibilistic evidence which is a possibility distribution as well as a body of evidence is proposed over an infinite universe of discourse. The inference with possibilistic evidence is investigated based on a…
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…