User contributions for RandomUndergrad
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8 April 2024
- 18:5218:52, 8 April 2024 diff hist +294 m Smallest Even Integer whose Euler Phi Value is not the Euler Phi Value of an Odd Integer No edit summary current
- 18:2418:24, 8 April 2024 diff hist 0 m Real Function with Strictly Negative Second Derivative is Strictly Concave No edit summary Tag: Reverted
1 April 2024
- 20:2020:20, 1 April 2024 diff hist +1 m Associative Law of Multiplication/Euclid's Proof No edit summary current
25 March 2024
- 04:3804:38, 25 March 2024 diff hist +8 Definition:Positive Definite Matrix No edit summary
21 March 2024
- 15:2015:20, 21 March 2024 diff hist −1 m Lagrange's Theorem (Number Theory) No edit summary current
7 March 2024
- 15:2515:25, 7 March 2024 diff hist +85 m Generalization to Dudeney's Distribution Problem Simplified proof and fixed grammar current
- 15:2115:21, 7 March 2024 diff hist −945 Generalization to Dudeney's Distribution Problem No edit summary
1 March 2024
- 02:0102:01, 1 March 2024 diff hist +94 m User:RandomUndergrad/Sandbox No edit summary current
- 01:5901:59, 1 March 2024 diff hist +1,595 N User:RandomUndergrad/Sandbox/Bounds to Recursive Functions Created page with "== Binet First Form == Consider $U_n = mU_{n-1} + U_{n-2}, U_0 = 0, U_1 = 1$, with $\Delta = \sqrt{m^2+4}, \alpha = \frac {m+\Delta}2, \beta = \frac {m-\Delta}2$. Then $U_n = \frac {\alpha^n - \beta^n}\Delta = \frac {\alpha^n - \beta^n}{\alpha - \beta} = \alpha^{n-1} + \alpha^{n-2}\beta + \dots + \beta^{n-1}$. Also $m\alpha^{n-2} \le U_n \le \alpha^{n-1}$, and $|m\beta^{2-n}| \le U_n \le |\beta^{1-n}|$ (at least for $m > 0$.) == Proof == Note that $\alpha \beta = \..." current
29 February 2024
- 17:5217:52, 29 February 2024 diff hist +2,790 N Generalization to Dudeney's Distribution Problem Created page with "== Theorem == Suppose $n > 1$ people, each with $a_1, a_2, \dots, a_n$ dollars, redistribute their wealth as follows: Going in order of their index, each person doubles everyone else's money by giving out their own money. If they all have the same amount of money after the process, the least positive integral solution is: :$a_j = 2^{j - 1} n + 1, \quad j = 1, \dots, n$ and each person will end up with $2^n$ dollars each. == Proof == Let us define the total amount o..."
- 05:3405:34, 29 February 2024 diff hist +2,102 N Upper Bound of Pell Number Created page with "== Theorem == For all $n \in \N$: :$P_n \le \paren {1 + \sqrt 2}^{n - 1}$ where: :$P_n$ is the $n$th Pell number == Proof == The proof proceeds by induction. For all $n \in \N$, let $\map P n$ be the proposition: :$P_n \le \paren {1 + \sqrt 2}^{n - 1}$ === Basis for the Induction === $\map P 1$ is true, as this just says: :$P_1 = 1 = \paren {1 + \sqrt 2}^0$ It is also..." current
- 05:0805:08, 29 February 2024 diff hist −25 m Fibonacci Number less than Golden Section to Power less One No edit summary current
28 February 2024
- 19:3119:31, 28 February 2024 diff hist +2,186 N Lower Bound of Pell Number Created page with "== Theorem == For all $n \in \N$: :$P_n \ge 2 \paren {1 + \sqrt 2}^{n - 2}$ where: :$P_n$ is the $n$th Pell number == Proof == The proof proceeds by induction. For all $n \in \N$, let $\map P n$ be the proposition: :$P_n \ge 2 \paren {1 + \sqrt 2}^{n - 2}$ === Basis for the Induction === $\map P 1$ is true, as this just says: :$P_1 = 1 = 2 \paren 2^{-1} \ge 2 \paren {1..."
- 19:2319:23, 28 February 2024 diff hist +161 Fibonacci Number greater than Golden Section to Power less Two No edit summary
26 February 2024
- 01:1901:19, 26 February 2024 diff hist −9 m Consecutive Fibonacci Numbers are Coprime No edit summary current
4 February 2024
- 23:5923:59, 4 February 2024 diff hist +1 m Successor is Supremum No edit summary
- 23:5923:59, 4 February 2024 diff hist +1 m Negation of Integer is Primitive Recursive No edit summary current
- 23:5823:58, 4 February 2024 diff hist +1 m Cowen's Theorem/Lemma 1 No edit summary current
- 23:5823:58, 4 February 2024 diff hist +1 m Characterization of Paracompactness in T3 Space/Lemma 15 No edit summary
- 23:5723:57, 4 February 2024 diff hist +1 m Characterization of Paracompactness in T3 Space/Lemma 6 No edit summary
- 23:5723:57, 4 February 2024 diff hist +1 m Bounded Lattice has Both Greatest Element and Smallest Element No edit summary
1 February 2024
- 18:3118:31, 1 February 2024 diff hist +744 Sides of Orthic Triangle of Obtuse Triangle/Proof No edit summary
- 17:5517:55, 1 February 2024 diff hist +377 Union of Intersections of 2 from 3 equals Intersection of Unions of 2 from 3 No edit summary current
- 16:4616:46, 1 February 2024 diff hist +1,247 Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Solution 2 No edit summary
- 16:4516:45, 1 February 2024 diff hist +265 Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Solution 2 No edit summary
25 January 2024
- 18:0318:03, 25 January 2024 diff hist +641 Square of Sample Correlation Coefficient is no greater than 1 No edit summary
- 17:3417:34, 25 January 2024 diff hist +124 Product of 5 Consecutive Integers is Divisible by 120 No edit summary
- 17:3317:33, 25 January 2024 diff hist +3 m Product of 3 Consecutive Integers is Divisible by 6 No edit summary
- 17:3317:33, 25 January 2024 diff hist +125 Product of 4 Consecutive Integers is Divisible by 24 No edit summary
- 17:3317:33, 25 January 2024 diff hist +121 Product of 3 Consecutive Integers is Divisible by 6 No edit summary
- 17:2117:21, 25 January 2024 diff hist +416 Cauchy Distribution is Symmetric about Median No edit summary
24 January 2024
- 19:4019:40, 24 January 2024 diff hist +71 Sum of nth Fibonacci Number over nth Power of 2/Proof 3 No edit summary
25 October 2023
- 16:2316:23, 25 October 2023 diff hist +1,846 Babbage's Congruence No edit summary current
- 03:3803:38, 25 October 2023 diff hist +12 m Logarithm of Power/Natural Logarithm/Natural Power No edit summary current
23 October 2023
- 04:1404:14, 23 October 2023 diff hist +916 N Equivalence of Definitions of Kurtosis Created page with "== Theorem == {{TFAE|def = Kurtosis}} === Definition 1 === {{:Definition:Kurtosis/Definition 1}} === Definition 2 === {{:Definition:Kurtosis/Definition 2}} == Proof == {{begin-eqn}} {{eqn | l = \expect{\paren {\frac {X - \mu} \sigma}^4} | r = \frac {\expect{\paren {X - \mu}^4} } {\sigma^4} | c = Expectation is Linear }} {{eqn | r = \frac {\expect{\paren {X - \mu}^4} } {\paren {\..." current
- 03:2803:28, 23 October 2023 diff hist +1,696 Excess Kurtosis of Continuous Uniform Distribution No edit summary current
- 02:1302:13, 23 October 2023 diff hist +85 Babbage's Congruence It would seem that the theorem can be extended to p=2 and a,b = 0.
- 01:5901:59, 23 October 2023 diff hist +2,491 Babbage's Congruence No edit summary
- 01:4901:49, 23 October 2023 diff hist +8 m Logarithm of Power/Natural Logarithm/Natural Power No edit summary
- 01:3201:32, 23 October 2023 diff hist 0 m Logarithm of Power/Natural Logarithm/Natural Power No edit summary
3 October 2023
- 18:3718:37, 3 October 2023 diff hist +1,780 Lamé's Theorem/Least Absolute Remainder No edit summary current
- 18:3618:36, 3 October 2023 diff hist +5,501 N Lamé's Theorem/Least Absolute Remainder/Lemma Created page with "== Theorem == Let $a, b \in \Z_{>0}$ be (strictly) positive integers. Let the Euclidean Algorithm: Least Absolute Remainder variant be employed to find the GCD of $a$ and $b$. <onlyinclude> Suppose it takes $n$ cycles around the Euclidean Algorithm: Least Absolute Remainder variant to find $\gcd \set {..." current
- 14:1814:18, 3 October 2023 diff hist −7 m Lamé's Theorem/Lemma No edit summary current
- 14:0814:08, 3 October 2023 diff hist 0 m Lamé's Theorem/Lemma No edit summary
15 August 2023
- 00:0600:06, 15 August 2023 diff hist +418 Equation for Perpendicular Bisector of Two Points in Complex Plane/Examples/2+i, 3-2i/Standard Form No edit summary
14 August 2023
- 23:5823:58, 14 August 2023 diff hist +1,633 N Equation for Perpendicular Bisector of Two Points in Complex Plane/Standard Form Created page with "== Theorem == Let $z_1, z_2 \in \C$ be complex numbers. Let $L$ be the perpendicular bisector of the straight line through $z_1$ and $z_2$ in the complex plane. <onlyinclude> $L$ can be expressed by the equation: :$\map \Re {z_2 - z_1} x + \map \Im {z_2 - z_1} y = \dfrac {\cmod {z_2}^2 - \cmod {z_1}^2} 2$ </onlyinclude> == Proof == Let $z_1$..." current
- 23:5823:58, 14 August 2023 diff hist +421 Equation for Perpendicular Bisector of Two Points in Complex Plane/Parametric Form 1 No edit summary current
7 July 2023
- 22:2222:22, 7 July 2023 diff hist 0 m Henry Ernest Dudeney/Puzzles and Curious Problems/86 - Digits and Cubes/Solution No edit summary current
8 June 2023
- 21:0821:08, 8 June 2023 diff hist +527 Numbers of form 31 x 16^n are sum of 16 4th Powers No edit summary
- 20:4120:41, 8 June 2023 diff hist +126 N Category:Limit to Infinity of Summation of Euler Phi Function over Square Created page with "{{SubjectCategory|result = Limit to Infinity of Summation of Euler Phi Function over Square}} Category:Euler Phi Function" current