Question

How can we get all positive integer solution for these two equations

score 61 · Answer 1 · 2020-02-11 15:11:05

61

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How can we get all positive integer solution for these two equations

Published on 11 Feb 2020 - 15:11

score 107 · Answer 2 · 2020-02-15 23:17:33

107

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Show that this pairing function is onto N

Published on 15 Feb 2020 - 23:17

score 47 · Answer 3 · 2020-02-19 09:16:23

47

Views

Is there a measure $\mu$ on $\mathbb{N}$ such that $\int_{\mathbb{N}}f \ \text{d}\mu = \sum_{n\in\mathbb{N}}a_{n}f(n)$?

Published on 19 Feb 2020 - 9:16

score 119 · Answer 4 · 2026-03-25 13:56:20

119

Views

Natural numbers inequality $na^{n-1}b\leq(n-1)a^n+b^n$ by induction

Published on 25 Mar 2026 - 13:56

score 623 · Answer 5 · 2020-02-27 11:31:32

623

Views

Cardinality of prime numbers

Published on 27 Feb 2020 - 11:31

score 69 · Answer 6 · 2020-03-01 17:25:22

69

Views

find the smallest $n>1$ such that : $n(n+1)(2n+1)=6m^{2}$

Published on 01 Mar 2020 - 17:25

score 86 · Answer 7 · 2020-03-02 09:01:13

86

Views

Subsets of the naturals

Published on 02 Mar 2020 - 9:01

score 266 · Answer 8 · 2026-03-25 22:10:49

266

Views

Is there a context-free language that can produce all the composite numbers?

Published on 25 Mar 2026 - 22:10

score 126 · Answer 9 · 2026-03-26 16:10:08

126

Views

Let $m,n$ be natural numbers. Then prove the commutativity of the product $n\times m = m\times n$.

Published on 26 Mar 2026 - 16:10

score 72 · Answer 10 · 2026-03-26 17:32:14

72

Views

How do we prove there is no natural number between $a$ and its successor $a\texttt{+}\texttt{+}$?

Published on 26 Mar 2026 - 17:32

score 124 · Answer 11 · 2020-03-08 16:54:10

124

Views

Solutions $(x, y),\;x,y\in \mathbb Z$ to the equation $x! +1 = y^2$

Published on 08 Mar 2020 - 16:54

score 89 · Answer 12 · 2020-03-08 20:15:09

89

Views

With $x = \sqrt{ \dfrac{97n+2}{2n-1} } $, find $n\in\mathbb{N}$ such that $x \in \mathbb{N}$.

Published on 08 Mar 2020 - 20:15

score 90 · Answer 13 · 2026-03-26 11:24:05

90

Views

Why is $\mathbb{N}$ well-ordered?

Published on 26 Mar 2026 - 11:24

score 189 · Answer 14 · 2020-03-12 07:44:32

189

Views

Polydivisible Pandigital Number in different bases

Published on 12 Mar 2020 - 7:44

score 146 · Answer 15 · 2026-03-26 17:31:33

146

Views

A question about Dedekind-infinite sets and Peano natural integers.

Published on 26 Mar 2026 - 17:31

List Question

How can we get all positive integer solution for these two equations

Show that this pairing function is onto N

Is there a measure $\mu$ on $\mathbb{N}$ such that $\int_{\mathbb{N}}f \ \text{d}\mu = \sum_{n\in\mathbb{N}}a_{n}f(n)$?

Natural numbers inequality $na^{n-1}b\leq(n-1)a^n+b^n$ by induction

Cardinality of prime numbers

find the smallest $n>1$ such that : $n(n+1)(2n+1)=6m^{2}$

Subsets of the naturals

Is there a context-free language that can produce all the composite numbers?

Let $m,n$ be natural numbers. Then prove the commutativity of the product $n\times m = m\times n$.

How do we prove there is no natural number between $a$ and its successor $a\texttt{+}\texttt{+}$?

Solutions $(x, y),\;x,y\in \mathbb Z$ to the equation $x! +1 = y^2$

With $x = \sqrt{ \dfrac{97n+2}{2n-1} } $, find $n\in\mathbb{N}$ such that $x \in \mathbb{N}$.

Why is $\mathbb{N}$ well-ordered?

Polydivisible Pandigital Number in different bases

A question about Dedekind-infinite sets and Peano natural integers.

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