My One Fiftieth Of A Dollar

Number Theory

An unexpected and enjoyable source of learning and knowledge for me has been the comment sections. Thanks to all for sharing what you know! Click Baiters Beware. Outside of doing videos, my resolute goal is to expose those who deceive for monetary gain. You will soon notice that mathematicians are not much more than mere alphabetical order junkies! I was disappointed to learn G.H. Hardy stated all chess problems are trivial! He did characterize chess as genuine mathematics. Doron Zeilberger called this snooty drivel.

Instructional Videos Algebra, Trigonometry, Calculus and Number Theory. Also videos related to critical thinking, logic, and general reasoning and problem solving.

Show 2‖(3^(2^n )+1) ∀ n ∈ N

Show 2‖(3^(2^n )+1) ∀ n ∈ N
Compute probability that a randomly chosen positive divisor of 15^49 is a multiple of 15^37

Compute probability that a randomly chosen positive divisor of 15^49 is a multiple of 15^37
Show that 2002^2002 can be expressed as the sum of four cubes, IMO short list 2003

Show that 2002^2002 can be expressed as the sum of four cubes, IMO short list 2003
Given f(x)=log∜3⁡(x) Suppose range of f(x) is [-16,-4] Find the domain of f(x)

Given f(x)=log∜3⁡(x) Suppose range of f(x) is [-16,-4] Find the domain of f(x)
x∈Z 0≤x≤78 45x≡13 (mod 79)

x∈Z 0≤x≤78 45x≡13 (mod 79)
Find x∈Ν, x between 1400 and 1500 x^7+x^6+x^5+x^4+x^3+x^2 ≡ 0 (mod 719)

Find x∈Ν, x between 1400 and 1500 x^7+x^6+x^5+x^4+x^3+x^2 ≡ 0 (mod 719)
Similar SMO Senior 2025 Problem 6 Find m,M such that m≤ (81+ 60sinxcosx + 80sin^2 (x)) ≤ M

Similar SMO Senior 2025 Problem 6 Find m,M such that m≤ (81+ 60sinxcosx + 80sin^2 (x)) ≤ M
Similar SMO Open 2025, #2 Find area of region bounded by graphs of x^2+y^2=81 and |x|+|y|=9

Similar SMO Open 2025, #2 Find area of region bounded by graphs of x^2+y^2=81 and |x|+|y|=9
A function f(x) satisfies f(4-x)+5f(x) = 4x^3+12x^2-40x+72 ∀ x∈R. Find f(x)

A function f(x) satisfies f(4-x)+5f(x) = 4x^3+12x^2-40x+72 ∀ x∈R. Find f(x)
Similar SMO Senior 2025, Problem 7 Find the largest coefficient when (5x^2+1/x)^7 is expanded

Similar SMO Senior 2025, Problem 7 Find the largest coefficient when (5x^2+1/x)^7 is expanded
Prove that 20 consecutive integers contain an integer that less than the sum of its proper divisors

Prove that 20 consecutive integers contain an integer that less than the sum of its proper divisors
Similar SMO Senior 2025 Problem 5 Find the local maximum value of (19x^2)/(x^2+18x+18)

Similar SMO Senior 2025 Problem 5 Find the local maximum value of (19x^2)/(x^2+18x+18)
Generalization SMO Senior 2025, Problem 2 Klog2^K (⁡√K ) + 2/log√K (⁡2) = log2⁡(M) Find M

Generalization SMO Senior 2025, Problem 2 Klog2^K (⁡√K ) + 2/log√K (⁡2) = log2⁡(M) Find M
Similar SMO Senior 2025, Problem 3 Find the maximum value of (cosθ)^2 - 30cosθ - 9

Similar SMO Senior 2025, Problem 3 Find the maximum value of (cosθ)^2 - 30cosθ - 9
Find all n ∈ Z^(≤0) such that 2|2n+1| ≤ 6|n-2| + 3n. Similar SMO Junior 2025 Problem 6

Find all n ∈ Z^(≤0) such that 2|2n+1| ≤ 6|n-2| + 3n. Similar SMO Junior 2025 Problem 6
2 by 2 linear system of equations with infinite number of solutions intended as Desmos SAT question

2 by 2 linear system of equations with infinite number of solutions intended as Desmos SAT question
The sum of the roots of (10b+6a)x^2 + (9a^2-25b^2 )x - 12ab=0 is (21a-35b)k Find the value of k

The sum of the roots of (10b+6a)x^2 + (9a^2-25b^2 )x - 12ab=0 is (21a-35b)k Find the value of k
m ∈ N is semiprime ∏d|m (d+1) = 1408. Find an integer m satisfying this PI Product Equation

m ∈ N is semiprime ∏d|m (d+1) = 1408. Find an integer m satisfying this PI Product Equation
Similar to Junior 2025 SMO Review Problem 5, Quadratic equation dice probability

Similar to Junior 2025 SMO Review Problem 5, Quadratic equation dice probability
Given a,b,c,d,e,f≥0 a+b+c+d+e+f=2 abc+abf+ace≥5/54, Find maximum value of aef+bcd+bdf+cde+def

Given a,b,c,d,e,f≥0 a+b+c+d+e+f=2 abc+abf+ace≥5/54, Find maximum value of aef+bcd+bdf+cde+def
Solve (x+4)(x+40)/(x+11)(x+33) = 2

Solve (x+4)(x+40)/(x+11)(x+33) = 2
Prove there are an infinite number of integers n such that σ(n-1) is greater than σ(n)

Prove there are an infinite number of integers n such that σ(n-1) is greater than σ(n)
Find x ∈ R x√x - √x = 26970

Find x ∈ R x√x - √x = 26970
Find polynomial P(x) with integer coefficients such that P(√7+√6) = √7-√6

Find polynomial P(x) with integer coefficients such that P(√7+√6) = √7-√6
Compute log⁡(33 - 8√17)/log⁡(33 + 8√17) Computing a Logarithmic Quotient From Definition

Compute log⁡(33 - 8√17)/log⁡(33 + 8√17) Computing a Logarithmic Quotient From Definition
Find the remainder when 6^33 is divided by 125 Similar to SMO 2025 Senior Mock problem 21

Find the remainder when 6^33 is divided by 125 Similar to SMO 2025 Senior Mock problem 21
y=|x+17/3|+|x-16/3| y=x^2-8x+39+c Find the value of c so two graphs intersect at only one point

y=|x+17/3|+|x-16/3| y=x^2-8x+39+c Find the value of c so two graphs intersect at only one point
Given 2‖(n∈N) Show n is not the difference of two squares

Given 2‖(n∈N) Show n is not the difference of two squares
How many digits of nine are in the seventh power of the integer formed by juxtaposing 60 nines?

How many digits of nine are in the seventh power of the integer formed by juxtaposing 60 nines?
Find the probability that a randomly selected 4 digit positive integer is a multiple of 72, SMO 2025

Find the probability that a randomly selected 4 digit positive integer is a multiple of 72, SMO 2025