Question

$m_i, n_j$ integers and $\{m_i\}_{i=1}^{k}\neq\{n_j\}_{j=1}^{k'}.$ Does $\sum\frac{1}{m_i}=\sum\frac{1}{n_j}\implies\sum m_i\neq\sum n_j?$

score 77 · Answer 1 · 2026-02-23 07:24:19

77

Views

$m_i, n_j$ integers and $\{m_i\}_{i=1}^{k}\neq\{n_j\}_{j=1}^{k'}.$ Does $\sum\frac{1}{m_i}=\sum\frac{1}{n_j}\implies\sum m_i\neq\sum n_j?$

Published on 23 Feb 2026 - 7:24

score 31 · Answer 2 · 2024-02-03 14:38:26

31

Views

Proving equivalence of two different induction definitions

Published on 03 Feb 2024 - 14:38

score 75 · Answer 3 · 2024-02-03 15:02:28

75

Views

Does $\exists\ n$ such that the first $2n$ digits of Thue Morse, $X_{2n},$ is the concatenated sequence $X_n X_n?$ If not then why not?

Published on 03 Feb 2024 - 15:02

score 125 · Answer 4 · 2024-02-05 09:35:53

125

Views

Any positive integer can be written as $2^{\sum_{k=1}^N n_k+m_k}+\sum_{i=1}^{N} 2^{\left(\sum_{k=i}^N n_k+m_{k+1}\right)}\left(2^{m_i}-1\right)$

Published on 05 Feb 2024 - 9:35

score 60 · Answer 5 · 2026-03-27 10:41:06

60

Views

Peano axioms - do we need a specific property to show that the principle of mathematical induction implies the "correct" set of natural numbers?

Published on 27 Mar 2026 - 10:41

score 89 · Answer 6 · 2024-02-07 09:22:53

89

Views

Show that the number $\frac{\sqrt{2021^4+2 \cdot 2020^2-4041^2}}{505 \cdot 1011}$ is natural and a perfect cube.

Published on 07 Feb 2024 - 9:22

score 126 · Answer 7 · 2024-02-12 14:59:38

126

Views

Determine $n\in N$ such that $\frac{3^n-2^n}{3^n+2^n}+\frac{5^n-3^n}{5^n+3^n} \leq \frac{5^n-2^n}{5^n+2^n}$ .

Published on 12 Feb 2024 - 14:59

score 261 · Answer 8 · 2024-02-12 17:27:24

261

Views

Existence of a Subset $S$ of $\mathbb{N}$ Where All but Finitely Many Natural Numbers Are Sums of Consecutive Elements of $S$

Published on 12 Feb 2024 - 17:27

score 62 · Answer 9 · 2024-02-14 03:55:12

62

Views

Understanding a step in a functional equation

Published on 14 Feb 2024 - 3:55

score 28 · Answer 10 · 2026-03-27 00:04:15

28

Views

Monoid morphisms between naturals with multiplication and naturals with addition

Published on 27 Mar 2026 - 0:04

score 67 · Answer 11 · 2024-02-23 17:11:30

67

Views

Subset of integers called by a somewhat ill-defined property

Published on 23 Feb 2024 - 17:11

score 65 · Answer 12 · 2024-02-24 16:42:10

65

Views

Solving a simple quadratic equation : $40x+3 = (x+14)(x+3)+(x+1)$

Published on 24 Feb 2024 - 16:42

score 90 · Answer 13 · 2026-03-27 00:58:02

90

Views

Order type of N and Q

Published on 27 Mar 2026 - 0:58

score 66 · Answer 14 · 2024-02-27 09:03:04

66

Views

An ordinal $\nu$ is a natural iff there is no injection $f$ of $\nu$ into $X$ in $\mathscr P(\nu)\setminus\{\nu\}$.

Published on 27 Feb 2024 - 9:03

score 133 · Answer 15 · 2024-02-27 17:29:52

133

Views

$a^2-2b^2=-73696$

Published on 27 Feb 2024 - 17:29

List Question

$m_i, n_j$ integers and $\{m_i\}_{i=1}^{k}\neq\{n_j\}_{j=1}^{k'}.$ Does $\sum\frac{1}{m_i}=\sum\frac{1}{n_j}\implies\sum m_i\neq\sum n_j?$

Proving equivalence of two different induction definitions

Does $\exists\ n$ such that the first $2n$ digits of Thue Morse, $X_{2n},$ is the concatenated sequence $X_n X_n?$ If not then why not?

Any positive integer can be written as $2^{\sum_{k=1}^N n_k+m_k}+\sum_{i=1}^{N} 2^{\left(\sum_{k=i}^N n_k+m_{k+1}\right)}\left(2^{m_i}-1\right)$

Peano axioms - do we need a specific property to show that the principle of mathematical induction implies the "correct" set of natural numbers?

Show that the number $\frac{\sqrt{2021^4+2 \cdot 2020^2-4041^2}}{505 \cdot 1011}$ is natural and a perfect cube.

Determine $n\in N$ such that $\frac{3^n-2^n}{3^n+2^n}+\frac{5^n-3^n}{5^n+3^n} \leq \frac{5^n-2^n}{5^n+2^n}$ .

Existence of a Subset $S$ of $\mathbb{N}$ Where All but Finitely Many Natural Numbers Are Sums of Consecutive Elements of $S$

Understanding a step in a functional equation

Monoid morphisms between naturals with multiplication and naturals with addition

Subset of integers called by a somewhat ill-defined property

Solving a simple quadratic equation : $40x+3 = (x+14)(x+3)+(x+1)$

Order type of N and Q

An ordinal $\nu$ is a natural iff there is no injection $f$ of $\nu$ into $X$ in $\mathscr P(\nu)\setminus\{\nu\}$.

$a^2-2b^2=-73696$

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