Number Theory
145 videos • 39,399 views • by Flammable Maths
1
Irrational to Irrational power is rational? A classic Abstract Algebra Proof
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2
Square Root of 2 is Irrational but not Transcendental
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3
Natural Numbers can be either Even OR Odd - 2 Proofs & Partition of the Positive Integers
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4
But WHY Exactly is Negative times Negative Positive?! [ Zero x Something is Zero ]
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5
e VS. π - But which One IS Actually Greater?! [ TOP 10 MOST BRUTAL ANIME BATTLES ]
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6
All Prime Numbers are Nearly Divisible by 6 ! [ Epic NUMBERPHILE Reacc video :0 ]
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7
There are Infinitely many Primes! - Euclid's Proof of the Infinitude of Primes
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8
Irrational to Irrational Power is Rational?! Another Example!
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9
SO COOL!!! The Arithmetic Derivative: How to DIFFERENTIATE Numbers
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10
e^π VS. π^e ?! But which one IS actually bigger?!
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11
How much does yo Momma weigh? AND WHAT EVEN IS 4+8?!
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12
Catalan's Constant and the Taylor Series of the Inverse Tangent! [ + Exploring Python and Desmos ]
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13
Revisiting the BASEL PROBLEM: Double Integral Representation on the Unit Square!
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14
A CRAZY Integral Representation of the Riemann Zeta Function! [ Unit Square Integral ]
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15
ζ(1) or The Harmonic Series Diverges - A flammable Proof [ + Python and Desmos ]
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16
γ - A BRILLIANT Putnam Integral Journey - Analytic Number Theory at its finest
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17
The Euler-Mascheroni Constant - An Epic Proof of Convergence!
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18
WONDERFUL 𝜋ntegral! A Putnam Extravaganza [ Basel Problem Integral Representation ]
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19
Expressing the Floor Function as a Superposition of Unit Step Functions!
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20
ZETA IN DISGUISE- An Awesome Floor Function Integral!
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21
ZETA GAMMA EXTRAVAGANZA! A Brilliant Putnam Integral Generalization!
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22
SON OF A PUTNAM BOI! Integrating a CRAZY Variant!
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23
The Cotangent's Series Expansion Derivation using FOURIER SERIES [ Mittag-Leffler Theorem ]
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24
Deriving EULER's INFINITE SINE PRODUCT using the Mittag-Leffler Pole Expansion of the Cotangent!
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25
ONE NEAT PROOF! Deriving the EULER DEFINITION of the Gamma Function!
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26
Gamma Function Euler Form, Complementary video!
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27
MULTIPLICATION 101 - But what even 𝐈𝐒 4*8 [ Math Snaccs #2 ]
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28
The Weierstrass Definition of the GAMMA FUNCTION! - Proving Equivalence!
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29
The Birds, Bees and the MEMES - Our Lord and Saviour -1/12 [ Math Snaccs #3 ]
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30
WAIT, WHAT?! DIFFERENTIATING x FACTORIAL x! - Introducing the Digamma Function
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31
The Digamma Function at Integer Values!
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32
But HOW did Euler do it?! A BEAUTIFUL Solution to the FAMOUS Basel Problem!
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33
Wallis' Product Formula - One Simple Proof!
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34
Integrating one E🅱IC Apery Boi - Papa's Improvised Session #4 [ integral ln(x)ln(x+1)/x ]
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35
An Integral Representation for the Digamma Function!
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36
Deriving the Infinite Product Representations for all the Trigonometric Functions!
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37
INTEGRAL FIGTHO DESU! Brother vs. Brother, Who wins?
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38
Calculating an AMAZING Limit! - Papa's Improvised Session #5
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39
Deriving one RIDICULOUS Integral Representation for the DIRICHLET ETA FUNCTION on the Unit Square!
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40
Euler's Reflection Formula - Two very ELEGANT Proofs!
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41
This is SERIESLY NUTS! Deriving the Sum of Reciprocals of the Odd Numbers Squared using INTEGRALS!
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42
i! and the Complex Gamma Function - Factorial 101 [ Math Snaccs #6 ]
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43
Calculating one BRUTAL Integral! Deriving Euler's Reflection Formula the RIDICULOUS way!
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44
Eulerian Integral of the First Kind - Deriving the BETA FUNCTION! [ The non-trigonometric Version ]
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45
The most FUN Series I EVER Evaluated! An Analytic Number Theory EXTRAVAGANZA!
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46
So good!: ONE Integral, TWO Solutions! [ Desmos and WA Insights included ]
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47
A MathVenture: The Fransén-Robinson Constant - The Journey Begins
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48
A MathVenture: The Fransén-Robinson Constant - Progress!
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49
A MathVenture: The Fransén-Robinson Constant - THE BIG CONCLUSION!
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50
The Beta Function: Deriving its TRIGONOMETRIC EQUIVALENT!
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51
Series Evaluation for the Sophisticated Gentleman
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52
Legendre's Duplication Formula - A simple Proof!
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53
PURE ALGEBRA! Calculating Series the FANCY way!
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54
Factorial's Asymptotic Expansion - DERIVING STIRLING'S FORMULA! [ +Desmos Insights ]
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55
Some Prerequisit Analysis on the Pochhammer Symbol
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56
Life at the Limit! A pair of pretty horrible looking Limits!
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57
Algebraic Manipulations: Translating the Basel Problem into pi^2/12 !
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58
An Absolutely Surprising Trig Identity!
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59
Proof without Words: Triangular Numbers / Little Gauss
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60
May the Convergence be with You - An Exciting Double Integral on the Unit Square
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61
Gauss' Multiplication Formula - An Elementary Proof without Stirling!
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62
An Easy derivation of the Polygamma Reflection Formula
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63
The Pi Function - An Overview of Identities
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64
WOW! The Most AMAZING Way of Solving an Integral Ever! Deriving Raabe's Integral Formula!
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65
The Infinite Product Expansion for the Beta Function
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66
Little Gauss, The Triangular Numbers and Some Variants
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67
The Gamma Function for Half Integer Values
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68
The Exponential Integral - An Introduction to Exponential Type Special Functions
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69
69420
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70
The Sine and Cosine Integrals
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71
One Fine Integarahl!
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72
Putnam goes Diophantine!
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73
Two very Gucci Limits
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74
The Most Beautiful Result.
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75
[Private video]
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76
One Sweet Number Theory Trick to Surprise your Friends!
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77
Infinity Factorial.
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78
Golden Times - The Most Harmonic kind of Series
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79
Um?... Integrating ζ
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80
Mathvengers: Eulergame
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81
Exponential Integral - Its Amazing Series Representation
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82
The Series Representation for the Sine and Cosine Integrals!
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83
Weird Addition [Gone Wrong] [Done Right]
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84
Integrals gOnE wRonG - Number Theory 101 [ Math Snaccs #7 ]
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85
''Euler's Formula'' for the Exponential and (Co)Sine Integrals!
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86
An Interesting Infinite Half-Angle Product Representation for the sin(x)
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87
This Result looks WAY TOO GOOD to be True! Transforming transcendental bois!
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88
Oily-Maccaroni: A Curious Limit Definition!
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89
HALF Fibonacci Number?!
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90
Riemann would be Proud - An exciting Infinite Series
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91
Euler's Significant Result...
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92
AIME 1 2015 Problem 3 - A Prime Example of a Perfect Cube
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93
Sum of Factorials.
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94
IMO, a Very Nice Number Theory Exercise.
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95
A Wonderful Math Exercise worth a Diamond.
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96
An Epic Gaussian Diamond Fraction [ Part 1 ]
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97
An Epic Gaussian Diamond Fraction [ Part 1 ]
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98
An Epic Gaussian Diamond Fraction - Solving the Recurrence Relation [ Part 2 ]
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99
3!=1+2+3 & n Factorial is not 1+...+n
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100
Pascal's Triangle & its Sum of Entries of Each Row [Binomial Theorem, Generating Polynomial]
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101
Pascal's Diamond.
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101
Pascal's Diamond.
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102
Dividorial.
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103
Sum of Fibonacci Numbers.
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104
An Ingenious Solution Strategy! [ Putnam 2018 A1 ]
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105
A Beautiful Visual Interpretation - The Sum of Squares of the Fibonacci Numbers.
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106
PyMath #1 - When Dividorial and π Meet - Their Beautiful Relationship
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107
73939133 - Probably the Most Interesting Prime Number [Part 1]
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108
73939133 - Probably the Most Interesting Prime Number [Part 2][PyMath #2]
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109
Feynman would be proud. A Wonderful Generalized Integral.
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110
Frullani's Integral Identity
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111
Gauss' Representation for the Digamma Function
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112
A Relaxing Differential Equation.
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113
Slaying a Monster: Binet's Second Formula for Log Gamma
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114
One Geometric Geometric Geometric Geometric ... Series - Papa's Improvised Session #16
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115
Matrix Factorial?!
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116
One Surprising Matrix Factorial Result!
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117
Fibonacci Factorial & the Most Unknown Mathematical Constant [ PyMath #5 ]
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118
Complete Elliptic Integral of the 1st Kind - Its Amazing Series Representation!
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119
Explain this, Science!
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120
Can Repeating Decimals be Irrational?
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121
And How would you Explain THIS, Science?!
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122
Spinning a Lego Wheel FAST
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123
Repeating Decimals using CALCULUS!
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124
But, How Do You Divide by 7?
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125
A Number Theory Paradox?
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126
0.9999... = 1 ?
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127
A Cambridge Interview Question
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128
Mathematics Gone Radical - Denesting Roots
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129
Thanks Ramanujan, very cool!
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130
4 Relaxing Number Theory Problems.
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131
Which one is Bigger? sqrt(2) or cbrt(3)? - An Interesting Cambridge Interview Question!
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132
7 is the only Prime followed by a Cube.
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133
How REAL Men do Fractions Explained
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134
My First Quartic Equation...
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135
A Groundbreaking Mathematical Result
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136
But, How Do You Divide by 11?
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137
5/7
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138
Dividing by 69 is nice.
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139
The Title of this Video is Left as an Exercise for the Viewer.
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140
Two Consecutive Integers are Always Coprime.
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141
Let the Annual Monster Slaying Commence!
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142
When Ramanujan gets Bored.
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143
1089
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144
Most Students FAIL to Solve this Problem Completely...
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145
The Best Integral on YouTube
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