Канал: Vladimir Sharich

May 24, 2024

May 24, 2024

2024-04-30 Fixing the code

2024-04-30 Fixing the code

2024-05-03 Starting the report

2024-05-03 Starting the report

2024-04-23 Implementing Fox and Rabbittiger chase via Object Oriented Programming

2024-04-23 Implementing Fox and Rabbittiger chase via Object Oriented Programming

2024-04-16 Duration of Random Fox and Random Rabbitiger chase on boards of different size

2024-04-16 Duration of Random Fox and Random Rabbitiger chase on boards of different size

2024-04-10 Random Fox and Random Rabbitiger

2024-04-10 Random Fox and Random Rabbitiger

2024-04-02 Presenting one's work and results

2024-04-02 Presenting one's work and results

2024-03-26 SIMC2.0-2022 Problem(s)

2024-03-26 SIMC2.0-2022 Problem(s)

2024-03-19 Game of Life Wars

2024-03-19 Game of Life Wars

GMT20240305 180405 Recording 3762x2104

GMT20240305 180405 Recording 3762x2104

GMT20240213 180504 Recording 3840x2160

GMT20240213 180504 Recording 3840x2160

GMT20240206 180440 Recording 3762x2104

GMT20240206 180440 Recording 3762x2104

GMT20240130 182059 Recording 3762x2104

GMT20240130 182059 Recording 3762x2104

iNT 01 09 A Pair of Typical Problems

iNT 01 09 A Pair of Typical Problems

iNT 01 08 A Numerical Example of Steps of the Euclidean Algorithm and Linear Representation of GCD

iNT 01 08 A Numerical Example of Steps of the Euclidean Algorithm and Linear Representation of GCD

iNT 01 07 GCD as the Result of Euclidean Algorithm

iNT 01 07 GCD as the Result of Euclidean Algorithm

iNT 01 06 Steps of the Euclidean Algorithm and Linear Representation of Remainders

iNT 01 06 Steps of the Euclidean Algorithm and Linear Representation of Remainders

iNT 03 09 Proof of Möbius Inversion Formula

iNT 03 09 Proof of Möbius Inversion Formula

iNT 03 05 Multiplicativity of Euler's Function Proof by Induction

iNT 03 05 Multiplicativity of Euler's Function Proof by Induction

iNT 03 03 An Amusing Property of Euler's Function

iNT 03 03 An Amusing Property of Euler's Function

iNT 03 02 Formula for Euler's Function

iNT 03 02 Formula for Euler's Function

iNT 04 09 An Elementary Proof of Wilson's Theorem

iNT 04 09 An Elementary Proof of Wilson's Theorem

iNT 04 08 Polynomial $x^p x$ and Wilson's Theorem

iNT 04 08 Polynomial $x^p x$ and Wilson's Theorem

iNT 04 07 Properties of Polynomials Over a Field of Remainders Modulo Prime Number

iNT 04 07 Properties of Polynomials Over a Field of Remainders Modulo Prime Number

iNT 04 06 Euler's Theorem

iNT 04 06 Euler's Theorem

iNT 04 05 An Elementary Proof of Fermat's Little Theorem

iNT 04 05 An Elementary Proof of Fermat's Little Theorem

iNT 04 04 Fermat's Little Theorem Statement and Example of Application

iNT 04 04 Fermat's Little Theorem Statement and Example of Application

iNT 04 03 A Pair of Typical Problems

iNT 04 03 A Pair of Typical Problems

iNT 04 02 Arithmetic Properties of Modular Congruence

iNT 04 02 Arithmetic Properties of Modular Congruence

iNT 04 01 Modular Congruence

iNT 04 01 Modular Congruence

iNT 05 04 Primitive Root

iNT 05 04 Primitive Root

iNT 05 03 Order of a Power of a Remainder

iNT 05 03 Order of a Power of a Remainder

iNT 05 02 Geometric Progression $1,a,a^2,a^3,…$

iNT 05 02 Geometric Progression $1,a,a^2,a^3,…$

iNT 05 01 Order of a Remainder

iNT 05 01 Order of a Remainder

iNT 05 09 Legendre Symbol and Its Properties

iNT 05 09 Legendre Symbol and Its Properties

iNT 05 08 Euler's Criterion

iNT 05 08 Euler's Criterion

iNT 05 07 The Number of Quadratic Remainders Modulo Prime Number

iNT 05 07 The Number of Quadratic Remainders Modulo Prime Number

iNT 05 06 Proof of Existence of a Primitive Root

iNT 05 06 Proof of Existence of a Primitive Root

iNT 05 05 A Pair of Examples of Applications of Primitive Root

iNT 05 05 A Pair of Examples of Applications of Primitive Root

iNT 06 07 Periodic Continued Fractions and Their Values

iNT 06 07 Periodic Continued Fractions and Their Values

iNT 06 08 Decomposition of a Quadratic Irrationality into a Continued Fraction

iNT 06 08 Decomposition of a Quadratic Irrationality into a Continued Fraction

iNT 06 05 Decomposition of a Rational Number into a Continued Fraction

iNT 06 05 Decomposition of a Rational Number into a Continued Fraction

iNT 06 04 Finite Continued Fractions and Their Values

iNT 06 04 Finite Continued Fractions and Their Values

iNT 06 03 Matrix Form of the Recurrence Relation and Its Determinant

iNT 06 03 Matrix Form of the Recurrence Relation and Its Determinant

iNT 06 01 Definition of Continuants

iNT 06 01 Definition of Continuants

iNT 06 02 Recurrence Relation for Continuants and Algebraic Continued Fraction

iNT 06 02 Recurrence Relation for Continuants and Algebraic Continued Fraction

iNT 07 07 Geometric Meaning of Convergents of a Continued Fraction

iNT 07 07 Geometric Meaning of Convergents of a Continued Fraction

iNT 07 04 Value of a Continued Fraction

iNT 07 04 Value of a Continued Fraction

iNT 07 03 Convergence of Convergents

iNT 07 03 Convergence of Convergents

iNT 07 02 Recurrent Relations for Convergents of a Continued Fraction

iNT 07 02 Recurrent Relations for Convergents of a Continued Fraction

iNT 07 01 Definition of Convergents of a Continued Fraction and Their Connection with the Continuant

iNT 07 01 Definition of Convergents of a Continued Fraction and Their Connection with the Continuant

iNT 08 04 Minkowski's Lemma

iNT 08 04 Minkowski's Lemma

iNT 08 06 Proof of the Fermat's Two Squares Theorem Part I from the Prime Number to a Quadratic Form

iNT 08 06 Proof of the Fermat's Two Squares Theorem Part I from the Prime Number to a Quadratic Form

iNT 08 05 А Typical Problem for the Minkowski's Lemma

iNT 08 05 А Typical Problem for the Minkowski's Lemma

iNT 08 02 Blichfeldt's Lemma

iNT 08 02 Blichfeldt's Lemma

iNT 08 03 An Example of a Statement Proved Using an Idea from the Proof of Blichfeldt's Lemma

iNT 08 03 An Example of a Statement Proved Using an Idea from the Proof of Blichfeldt's Lemma

iNT 08 01 The Geometric Pigeonhole Principle

iNT 08 01 The Geometric Pigeonhole Principle

iNT 09 10 Weyl's Theorem Proof Part III Grasshopper Schizophrenia

iNT 09 10 Weyl's Theorem Proof Part III Grasshopper Schizophrenia

iNT 09 08 Weyl's Theorem Proof Part I Estimates for the Number of Jumps into the Interval Within One

iNT 09 08 Weyl's Theorem Proof Part I Estimates for the Number of Jumps into the Interval Within One

iNT 09 09 Weyl's Theorem Proof Part II Estimates for the Number of Jumps into the Interval Within Ma

iNT 09 09 Weyl's Theorem Proof Part II Estimates for the Number of Jumps into the Interval Within Ma

iNT 09 07 Distribution of sinn, Where n∈ℕ

iNT 09 07 Distribution of sinn, Where n∈ℕ

iNT 09 01 The Set of Values of {n𝛼} for a Rational 𝛼

iNT 09 01 The Set of Values of {n𝛼} for a Rational 𝛼

iNT 11 01 Properties of Pythagorean Triples

iNT 11 01 Properties of Pythagorean Triples

iNT 11 03 The Remainders Method

iNT 11 03 The Remainders Method

iNT 11 04 The Decomposition Method

iNT 11 04 The Decomposition Method

iNT 11 05 The Infinite Descent Method

iNT 11 05 The Infinite Descent Method

iNT 11 06 The Descent Method

iNT 11 06 The Descent Method

iNT 11 08 Equation 2^x+1=p^k and Fermat's Primes

iNT 11 08 Equation 2^x+1=p^k and Fermat's Primes

iNT 11 09 Equation 3^x 2^y=1 and Catalan's Conjecture

iNT 11 09 Equation 3^x 2^y=1 and Catalan's Conjecture

iNT 10 02 Linear Diophantine Equation Two Unknowns General Case

iNT 10 02 Linear Diophantine Equation Two Unknowns General Case

iNT 10 01 Linear Diophantine Equation with Mutualy Prime Coefficients Two Unknowns

iNT 10 01 Linear Diophantine Equation with Mutualy Prime Coefficients Two Unknowns

iNT 10 03 An Example of a Linear Diophantine Equation with Three Unknowns

iNT 10 03 An Example of a Linear Diophantine Equation with Three Unknowns

iNT 10 04 Linear Diophantine Equation Three Unknowns Existence of a Solution

iNT 10 04 Linear Diophantine Equation Three Unknowns Existence of a Solution

iNT 10 06 Chinese Remainders Theorem Statement

iNT 10 06 Chinese Remainders Theorem Statement

iNT 10 07 Chinese Remainders Theorem Proof by Induction

iNT 10 07 Chinese Remainders Theorem Proof by Induction

iNT 12 03 Division in the Ring ℤ√a

iNT 12 03 Division in the Ring ℤ√a

iNT 12 02 The Ring ℤ√a Closedness With Respect to +, ,•

iNT 12 02 The Ring ℤ√a Closedness With Respect to +, ,•

iNT 12 08 Existence of a Non Trivial Solution of Pell's Equation Part I a Hyperbola with Infinitely

iNT 12 08 Existence of a Non Trivial Solution of Pell's Equation Part I a Hyperbola with Infinitely

iNT 12 09 Existence of a Non Trivial Solution of Pell's Equation Part II a Specific Pair of Points

iNT 12 09 Existence of a Non Trivial Solution of Pell's Equation Part II a Specific Pair of Points

iNT 12 10 Existence of a Non Trivial Solution of Pell's Equation Part III the Quotient

iNT 12 10 Existence of a Non Trivial Solution of Pell's Equation Part III the Quotient

iNT 09 02 The Set of Values of {n𝛼} for an Irrational 𝛼 Kronecker's Theorem

iNT 09 02 The Set of Values of {n𝛼} for an Irrational 𝛼 Kronecker's Theorem

iNT 09 03 sup{sin n n∈ℕ}

iNT 09 03 sup{sin n n∈ℕ}

iNT 09 04 A Blind Hunter and Round Rabbits on the Integer Lattice

iNT 09 04 A Blind Hunter and Round Rabbits on the Integer Lattice

iNT 09 05 Weyl's Theorem Statement

iNT 09 05 Weyl's Theorem Statement

iNT 09 06 First Digits of Powers of Two

iNT 09 06 First Digits of Powers of Two

iNT 12 07 Solutions Form a Geometric Progression In Some Sense

iNT 12 07 Solutions Form a Geometric Progression In Some Sense

iNT 12 06 There Are Infinitely Many Solutions

iNT 12 06 There Are Infinitely Many Solutions

iNT 12 04 Invertible Elements of the Ring ℤ√a and Pell's equations

iNT 12 04 Invertible Elements of the Ring ℤ√a and Pell's equations

iNT 12 05 The Meaning of Signs

iNT 12 05 The Meaning of Signs

iNT 12 01 The Set ℤ√a and Uniqueness of the Representation

iNT 12 01 The Set ℤ√a and Uniqueness of the Representation

iNT 10 08 Chinese Remainders Theorem Constructive Proof

iNT 10 08 Chinese Remainders Theorem Constructive Proof

iNT 10 05 Sylvester's Theorem

iNT 10 05 Sylvester's Theorem

iNT 05 10 2!p, Law of Quadratic Reciprocity Statements and Example of Application

iNT 05 10 2!p, Law of Quadratic Reciprocity Statements and Example of Application

iNT 03 07 Number of Divisors and Sum of Divisors of a Positive Integer

iNT 03 07 Number of Divisors and Sum of Divisors of a Positive Integer

iNT 03 04 Multiplicativity of Euler's Function as a Corollary of the Formula

iNT 03 04 Multiplicativity of Euler's Function as a Corollary of the Formula

iNT 03 01 Definition of Euler's Function

iNT 03 01 Definition of Euler's Function

iNT 02 07 Uniqueness of Prime Factorization Statement

iNT 02 07 Uniqueness of Prime Factorization Statement

iNT 06 06 Decomposition of an Irrational Number into a Continued Fraction

iNT 06 06 Decomposition of an Irrational Number into a Continued Fraction

iNT 02 04 Existence of a Prime Factorization Statement

iNT 02 04 Existence of a Prime Factorization Statement

iNT 02 01 Indecomposable Elements

iNT 02 01 Indecomposable Elements

iNT 01 05 Theorem on the Linear Representation of GCD

iNT 01 05 Theorem on the Linear Representation of GCD

iNT 03 08 Möbius Function

iNT 03 08 Möbius Function

iNT 03 06 Formula for Euler's Function as a Corollary of the Multiplicativity

iNT 03 06 Formula for Euler's Function as a Corollary of the Multiplicativity

iNT 11 07 Perfect Numbers

iNT 11 07 Perfect Numbers

iNT 11 02 General Formulae for Pythagorean Triples

iNT 11 02 General Formulae for Pythagorean Triples

iNT 08 07 Proof of the Fermat's Two Squares Theorem Part II Properties of the Figure, Given by the I

iNT 08 07 Proof of the Fermat's Two Squares Theorem Part II Properties of the Figure, Given by the I

iNT 07 06 A4 Size

iNT 07 06 A4 Size

iNT 07 05 Rational Approximations of Irrational Numbers

iNT 07 05 Rational Approximations of Irrational Numbers

iNT 01 10 A Direct Proof of Existence of Linear Representation of GCD

iNT 01 10 A Direct Proof of Existence of Linear Representation of GCD

iNT 02 12 Fermat's Two Squares Theorem (Proof via Uniqueness of Prime Factorization)

iNT 02 12 Fermat's Two Squares Theorem (Proof via Uniqueness of Prime Factorization)

iNT-01-02 Definition of Euclidean Rings

iNT-01-02 Definition of Euclidean Rings

iNT-01-01 Divisibility, Invertible Elements, Associated Elements

iNT-01-01 Divisibility, Invertible Elements, Associated Elements

iNT 02 11 Wilson's Theorem and Its Corollary

iNT 02 11 Wilson's Theorem and Its Corollary

iNT 02 09 А Typical Problem

iNT 02 09 А Typical Problem

iNT 02 03 In Euclidean Rings All Indecomposable Elements Are Prime

iNT 02 03 In Euclidean Rings All Indecomposable Elements Are Prime

iNT 02 08 Uniqueness of Prime Factorization (Proof)

iNT 02 08 Uniqueness of Prime Factorization (Proof)

iNT 02 06 Prime Factorization of Complex Integers

iNT 02 06 Prime Factorization of Complex Integers

iNT 02 02 Prime Elements

iNT 02 02 Prime Elements

iNT 02 05 Existence of a Prime Factorization (Proof)

iNT 02 05 Existence of a Prime Factorization (Proof)

iNT 02 10 Fermat's Two Squares Theorem (Statement)

iNT 02 10 Fermat's Two Squares Theorem (Statement)

iNT 01 04 Definition of Greatest Common Divisor

iNT 01 04 Definition of Greatest Common Divisor

iNT 01 03 Complex Integers Form a Euclidean Ring

iNT 01 03 Complex Integers Form a Euclidean Ring