1 citations · 2 across the 14 of their papers we have counts for
14 papers
On the Ribenboim-Landau Conjecture
Felix Sidokhine
We prove the Ribenboim hypothesis, which states that if, starting from some integer , consecutive prime numbers , satisfy the inequality $\sqrt {p_ {n+1}}-\sqr…
Shnirelman's Theorem Applications
Felix Sidokhine
Shnirelman's theorem is applied to solving Diophantine equations, and also discussing of the problems of a representation of Gaussian integers by a sum of odd Gaussian primes.
Goldbach's Conjecture and Euler's -Function
Felix Sidokhine
In this paper we propose an alternative formulation of the binary and ternary Goldbach conjectures as the systems of equations involving the Euler -function.
Quartic Equations with Trivial Solutions over Gaussian Integers
Felix Sidokhine
In our work we study the equations of the form over Gaussian integers by a method of the resolvents. We study as a new equations (M…
Quadratic Equations in Three Variables over Gaussian Integers
Felix Sidokhine
We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.
Fermat's Last Theorem: Algebra, Geometry, and Number Theory
Felix Sidokhine
In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra, geometry and number theory
Fermat's Last Theorem: Algebra and Number Theory
Felix Sidokhine
In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.
Diophantine Inequalities with Primes, Auxiliary Inequalities, Evaluations of the Difference between Consecutive Primes
Felix Sidokhine
The goal of the present paper is to present a method of proving of Diophantine inequalities with primes through the use of auxiliary inequalities and available evaluations of the d…
On the Difference between Consecutive Primes and Estimates of the Number of Primes in the Interval
Felix Sidokhine
Using evaluations of the difference between consecutive primes we develop another way of estimating of the number of primes in the interval . We also discuss the ultra Cra…
On Proving of Diophantine Inequalities with Prime Numbers by Evaluations of the Difference between Consecutive Primes
Felix Sidokhine
Using as the working hypothesis of an evaluation of the difference between primes we represent in detail the proofs of Legendre's and Oppermann's co…
Diophantine Inequalities as a Problem of Difference between Consecutive Primes
Felix Sidokhine
In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}. Usi…
A Note on Quartic Equations with only Trivial Solutions
Felix Sidokhine
In our notice we propose the classification of some quartic equations with only trivial solutions by the auxiliary equations. For proving trivial solutions of the quartic equations…
An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method
Felix Sidokhine
The goal of this notice is to present a proof of Bachet's conjecture based exclusively on the fundamental theorem of arithmetic. The novelty of this proof consists in its introduct…
A Universal Quaternary Quadratic Form over Gaussian Integers
Felix Sidokhine
In this article we show that the form represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field e…