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- 21:13, 10 July 2020 St. Ives Problem/Fibonacci Variant (hist) [1,618 bytes] Prime.mover (talk | contribs) (Created page with "== Classic Problem == <onlyinclude> :$7$ old women are travelling to Rome. :Each old woman has $7$ mules. :On each mule are $7$ sacks. :In each sack are $7$ loaves of bread. :...")
- 19:17, 10 July 2020 2601 as Sum of 3 Squares in 12 Different Ways/Mistake (hist) [878 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Curious and Interesting Numbers|1997|David Wells|ed = 2nd|edpage = Second Edition}}: :The Dictionary ::$2601$ == Mistake == <onlyinclude>...")
- 14:23, 10 July 2020 Space of Continuously Differentiable on Closed Interval Real-Valued Functions with Pointwise Addition and Pointwise Scalar Multiplication form Vector Space (hist) [3,104 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $I := \closedint a b$ be a closed real interval. Let $\map \CC I$ be a Definition:Space of Continuous on Closed Inter...")
- 07:42, 10 July 2020 74,162/Mistake (hist) [1,546 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Curious and Interesting Numbers|1997|David Wells|ed = 2nd|edpage = Second Edition}}: :The Dictionary ::$74,162$ == Mistake == <onlyinclude...")
- 04:42, 10 July 2020 Largest Number not Expressible as Sum of Multiples of Coprime Integers (hist) [3,783 bytes] RandomUndergrad (talk | contribs) (Created page with "== Theorem == Let $a, b$ be coprime integers, each greater than $1$. Then the largest number not expressible as a sum of multiples of $a$ and...")
- 11:07, 9 July 2020 Prime Decomposition of 10th Fermat Number/Historical Note (hist) [2,619 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Prime Decomposition of 8th Fermat Number == <onlyinclude> $F_{10}$ was proved composite in $1952$ by {{AuthorRef|Raph...")
- 10:18, 9 July 2020 Squares Ending in n Occurrences of m-Digit Pattern/Example (hist) [2,624 bytes] RandomUndergrad (talk | contribs) (Created page with "== Example of Squares Ending in n Occurrences of m-Digit Pattern == <onlyinclude> The $n$th term in the sequence: :$611, 734 \, 611, 494 \, 734 \, 611, 63 \, 494 \, 734 \...")
- 10:18, 9 July 2020 Squares Ending in n Occurrences of m-Digit Pattern (hist) [5,777 bytes] RandomUndergrad (talk | contribs) (Created page with "== Theorem == Suppose there exists some integer $x$ such that $x^2$ ends in some $m$-digit pattern ending in an Definition:Odd I...")
- 10:07, 9 July 2020 Prime Decomposition of 10th Fermat Number (hist) [3,198 bytes] Prime.mover (talk | contribs) (Created page with "{{begin-eqn}} {{eqn | l = 2^{\paren {2^{10} } } + 1 | r = 179 \, 769 \, 313 \, 486 \, 231 \, 590 \, 772 \, 930 \, 519 \, 078 \, 902 \, 473 \, 361 \, 797 \, 697 \, 894 \,...")
- 07:31, 9 July 2020 Numbers n whose Euler Phi value Divides n + 1/Mistake/Second Edition (hist) [2,216 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Unsolved Problems in Number Theory|1994|Richard K. Guy|ed = 2nd|edpage = Second Edition}}: :$\mathbf B$: Divisibility ::$\mathbf {B 37}$: Do...")
- 07:11, 9 July 2020 Numbers n whose Euler Phi value Divides n + 1/Mistake/Third Edition (hist) [2,172 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Unsolved Problems in Number Theory|2004|Richard K. Guy|ed = 3rd|edpage = Third Edition}}: :$\mathbf B$: Divisibility ::$\mathbf {B 37}$: Doe...") originally created as "Numbers n whose Euler Phi value Divides n + 1/Mistake"
- 17:56, 8 July 2020 Wilson's Theorem/Corollary 2/Proof 2 (hist) [1,361 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Wilson's Theorem/Corollary 2}} == Proof == <onlyinclude> Consider the numbers of $\set {1, 2, \ldots, n}$ which are not Definition:Integer Multiple|multipl...")
- 17:54, 8 July 2020 Wilson's Theorem/Corollary 2/Proof 1 (hist) [2,888 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Wilson's Theorem/Corollary 2}} == Proof == <onlyinclude> Proof by induction: Let $\map P n$ be the proposition: :$\d...")
- 14:25, 8 July 2020 Real Sequence/Examples/Arbitrary Sequence 2 (hist) [739 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Real Sequence == <onlyinclude> The recurrence relation: :$s_n = \begin {cases} 1 & : n = 1 \\ 0...")
- 08:19, 8 July 2020 Real Sequence/Examples/(1 + (-1)^n) / 2 (hist) [628 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Real Sequence == <onlyinclude> The real sequence whose first few terms...")
- 07:13, 8 July 2020 Real Sequence/Examples/n (hist) [611 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Real Sequence == <onlyinclude> The real sequence whose first few terms...")
- 07:04, 8 July 2020 Real Sequence/Examples/(-1)^n 2^(-n) (hist) [669 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Real Sequence == <onlyinclude> The real sequence whose first few terms...")
- 05:23, 8 July 2020 Real Sequence/Examples/n over (n+1) (hist) [650 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Real Sequence == <onlyinclude> The real sequence whose first few terms...")
- 21:59, 7 July 2020 Range of Infinite Sequence may be Finite (hist) [901 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\sequence {x_n}_{n \mathop \in \N}$ be an infinite sequence. Then it is possible for the Definition:Range of Sequence|r...")
- 14:02, 7 July 2020 Sum of Unitary Divisors of Integer (hist) [983 bytes] RandomUndergrad (talk | contribs) (Created page with "== Theorem == Let $n$ be an integer such that $n \ge 2$. Let $\map {\sigma^*} n$ be the sum of all positive Definition:Unitary Divisor|unitary divis...")
- 14:02, 7 July 2020 Sum of Unitary Divisors is Multiplicative (hist) [2,829 bytes] RandomUndergrad (talk | contribs) (Created page with "== Theorem == Let $\map {\sigma^*} n$ denote the sum of unitary divisors of $n$. Then the function: :$\displaystyle \sigma^*: \Z_{>0} \to \Z_{...")
- 14:02, 7 July 2020 Sum of Unitary Divisors of Power of Prime (hist) [978 bytes] RandomUndergrad (talk | contribs) (Created page with "== Theorem == Let $n = p^k$ be the power of a prime number $p$. Then the sum of all Definition:Positive Integer|...")
- 08:32, 7 July 2020 Leigh.Samphier/Sandbox/Doubleton of Elements is Subset (hist) [817 bytes] Leigh.Samphier (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $S$ be a set. Let $\set {x,y}$ be the doubleton of $x$ and $y$. Then: :$x, y \in S \iff \set {x,...")
- 07:53, 7 July 2020 Triples with Same Sum and Same Product/Mistake (hist) [1,566 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Unsolved Problems in Number Theory|2004|Richard K. Guy|ed = 3rd|edpage = Third Edition}}: :$\text D 16$: Triples with Same Sum and Same Prod...")
- 06:04, 7 July 2020 Smallest Integer which is Product of 4 Triples all with Same Sum/Historical Note (hist) [2,269 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Smallest Number which is Sum of 4 Triples with Equal Products == <onlyinclude> {{AuthorRef|David Wells}}, in his {{BookLink|Curious and Interesting N...")
- 05:51, 7 July 2020 Smallest Number which is Sum of 4 Triples with Equal Products/Mistake (hist) [1,430 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Curious and Interesting Numbers|1997|David Wells|ed = 2nd|edpage = Second Edition}}: :The Dictionary ::$118$ == Mistake == <onlyinclude> :...")
- 22:00, 6 July 2020 Existence of Square Roots of Positive Real Number/Examples/Square Root of 2 (hist) [592 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Existence of Square Roots of Positive Real Number == <onlyinclude> There exists $u \in \R$ such that $u^2 = 2$. </onlyinclude> == Proof == {{ProofW...")
- 21:57, 6 July 2020 Existence of Square Roots of Positive Real Number/Examples (hist) [358 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Existence of Square Roots of Positive Real Number == <onlyinclude> === Existence of Square Roots of Positive Real Number/Examples/Square Root of 2|...")
- 21:32, 6 July 2020 Supremum of Subset of Real Numbers/Examples/Left Half Open Interval from 0 to 1 (hist) [1,125 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Supremum of Subset of Real Numbers == <onlyinclude> Let $\hointl 0 1$ denote the Definition:Left Half-Open Re...")
- 21:31, 6 July 2020 Supremum of Subset of Real Numbers/Examples/Strictly Negative Real Numbers (hist) [1,148 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Supremum of Subset of Real Numbers == <onlyinclude> Let $\R_{<0}$ be the Definition:Strictly Negative Real Nu...")
- 20:55, 6 July 2020 Bounded Below Subset of Real Numbers/Examples/Left Half Open Interval from 0 to 1 (hist) [792 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Bounded Below Subset of Real Numbers == <onlyinclude> Let $I$ be the Definition:Left Half-Open Real Interva...")
- 20:53, 6 July 2020 Bounded Below Subset of Real Numbers/Examples/Strictly Negative Real Numbers (hist) [757 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Unbounded Below Subset of Real Numbers == <onlyinclude> Let $I$ be the Definition:Unbounded Open Real Int...")
- 20:53, 6 July 2020 Bounded Above Subset of Real Numbers/Examples/Left Half Open Interval from 0 to 1 (hist) [792 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Bounded Above Subset of Real Numbers == <onlyinclude> Let $I$ be the Definition:Left Half-Open Real Interva...")
- 20:51, 6 July 2020 Bounded Above Subset of Real Numbers/Examples/Strictly Negative Real Numbers (hist) [810 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Bounded Above Subset of Real Numbers == <onlyinclude> Let $I$ be the Definition:Unbounded Open Real Interva...")
- 20:43, 6 July 2020 Bounded Below Subset of Real Numbers/Examples/Real Numbers (hist) [1,196 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Unbounded Below Subset of Real Numbers == <onlyinclude> Let $\R$ denote the Definition:Real Number|set of...")
- 20:43, 6 July 2020 Bounded Above Subset of Real Numbers/Examples/Real Numbers (hist) [720 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Unbounded Above Subset of Real Numbers == <onlyinclude> Let $\R$ denote the Definition:Real Number|set of...")
- 12:26, 6 July 2020 Leigh.Samphier/Sandbox/Power Set of Doubleton (hist) [1,615 bytes] Leigh.Samphier (talk | contribs) (Created page with "== Theorem == Let $x, y$ bedistinct objects. Then the power set of the Definition:Doubleton|doublet...")
- 07:46, 6 July 2020 Cheryl's Birthday (hist) [5,130 bytes] Prime.mover (talk | contribs) (Created page with "== Classic Problem == Albert and Bernard have just become friends with Cheryl. They both want to know when her birthday is. Cheryl tells both of them that it is one of the...")
- 21:17, 5 July 2020 Adjugate Matrix/Examples/Arbitrary Matrix 4 (hist) [3,865 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Adjugate Matrix == <onlyinclude> Let $\mathbf A$ be the square matrix: :$\mathbf A = \begin {pmatrix...")
- 11:58, 5 July 2020 Space of Continuous on Closed Interval Real-Valued Functions with Pointwise Addition and Pointwise Scalar Multiplication form Vector Space (hist) [5,226 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $I := \closedint a b$ be a closed real interval. Let $\map \CC I$ be a Definition:Space of Continuous on Closed Inter...")
- 11:04, 5 July 2020 Adjugate Matrix/Examples/Arbitrary Matrix 3 (hist) [4,646 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Adjugate Matrix == <onlyinclude> Let $\mathbf A$ be the square matrix: :$\mathbf A = \begin {pmatrix...")
- 10:02, 5 July 2020 Adjugate Matrix/Examples/Arbitrary Matrix 2 (hist) [4,691 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Adjugate Matrix == <onlyinclude> Let $\mathbf A$ be the square matrix: :$\mathbf A = \begin {pmatrix...")
- 09:35, 5 July 2020 Adjugate Matrix/Examples/Arbitrary Matrix 1 (hist) [6,110 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Adjugate Matrix == <onlyinclude> Let $\mathbf A$ be the square matrix: :$\mathbf A = \begin {pmatrix...")
- 07:29, 5 July 2020 Simultaneous Linear Equations/Examples/Arbitrary System 12 (hist) [2,702 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Simultaneous Linear Equations == <onlyinclude> Let $S$ denote the system of Definition:Simultaneous Linear Equatio...")
- 07:17, 5 July 2020 Simultaneous Linear Equations/Examples/Arbitrary System 11 (hist) [3,193 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Simultaneous Linear Equations == <onlyinclude> Let $S$ denote the system of Definition:Simultaneous Linear Equatio...")
- 23:31, 4 July 2020 Simultaneous Linear Equations/Examples/Arbitrary System 10 (hist) [2,899 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Simultaneous Linear Equations == <onlyinclude> Let $S$ denote the system of Definition:Simultaneous Linear Equatio...")
- 23:10, 4 July 2020 Simultaneous Linear Equations/Examples/Arbitrary System 9 (hist) [2,933 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Simultaneous Linear Equations == <onlyinclude> Let $S$ denote the system of Definition:Simultaneous Linear Equatio...")
- 22:52, 4 July 2020 Simultaneous Linear Equations/Examples/Arbitrary System 8 (hist) [2,675 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Simultaneous Linear Equations == <onlyinclude> Let $S$ denote the system of Definition:Simultaneous Linear Equatio...")
- 22:11, 4 July 2020 Simultaneous Linear Equations/Examples/Arbitrary System 7 (hist) [3,305 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Simultaneous Linear Equations == <onlyinclude> Let $S$ denote the system of Definition:Simultaneous Linear Equatio...")
- 21:16, 4 July 2020 Matrix Scalar Product Distributes over Number Addition/Proof (hist) [1,053 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Matrix Scalar Product Distributes over Number Addition}} == Proof == <onlyinclude> {{begin-eqn}} {{eqn | l = \paren {\lambda + \mu} \mathbf A | r = \pa...")