Question

Prove that every number to a power greater than 1 can be written as $X^{n+1} = \Sigma_{i=1}^{n}(a_{i}X^{i}-b_{i}Y^{i})$

score 65 · Answer 1 · 2019-04-02 15:21:49

65

Views

Prove that every number to a power greater than 1 can be written as $X^{n+1} = \Sigma_{i=1}^{n}(a_{i}X^{i}-b_{i}Y^{i})$

Published on 02 Apr 2019 - 15:21

score 1.9k · Answer 2 · 2019-04-05 17:59:06

1.9k

Views

Does the average primeness of natural numbers tend to zero?

Published on 05 Apr 2019 - 17:59

score 71 · Answer 3 · 2019-04-06 04:18:45

71

Views

Generations of a counting sequence

Published on 06 Apr 2019 - 4:18

score 641 · Answer 4 · 2019-04-10 06:46:00

641

Views

sum of the first $n^2$ natural numbers closed form

Published on 10 Apr 2019 - 6:46

score 165 · Answer 5 · 2019-04-10 21:20:03

165

Views

An apparently harmless exercise concerning induction

Published on 10 Apr 2019 - 21:20

score 422 · Answer 6 · 2019-04-12 15:27:45

422

Views

Are there $2^{\aleph_{0} }$ sets of natural numbers such that each two have finite intersection

Published on 12 Apr 2019 - 15:27

score 56 · Answer 7 · 2019-04-17 09:58:55

56

Views

Generalised Divisibility

Published on 17 Apr 2019 - 9:58

score 251 · Answer 8 · 2026-02-23 05:18:59

251

Views

Proof of equivalence between two methods of binary to decimal conversion.

Published on 23 Feb 2026 - 5:18

score 85 · Answer 9 · 2026-03-25 04:42:37

85

Views

Prove that when writing up all even numbers in a column, then chaining $2n+1$ from them, we get all natural numbers exactly once.

Published on 25 Mar 2026 - 4:42

score 56 · Answer 10 · 2019-04-22 21:27:05

56

Views

Show that a number $n$ is divisible by 6 if and only if it can be written as a sum of three distinct divisors.

Published on 22 Apr 2019 - 21:27

score 94 · Answer 11 · 2019-04-23 00:05:21

94

Views

Is it true that $n \leq 2^{n-1}$ for all natural numbers $n > 0$?

Published on 23 Apr 2019 - 0:05

score 287 · Answer 12 · 2026-03-25 06:06:30

287

Views

In Non-standard analysis, is the number of natural numbers a hyperreal number?

Published on 25 Mar 2026 - 6:06

score 69 · Answer 13 · 2026-03-26 02:47:54

69

Views

Properties of this notion of density in $\Bbb{N}$?

Published on 26 Mar 2026 - 2:47

score 159 · Answer 14 · 2026-03-25 07:49:05

159

Views

General Solution of Linear Diophantine Equation with 2 and more than 2 variable

Published on 25 Mar 2026 - 7:49

score 550 · Answer 15 · 2019-05-05 12:13:48

550

Views

Quadratic equation with natural number coefficients

Published on 05 May 2019 - 12:13

List Question

Prove that every number to a power greater than 1 can be written as $X^{n+1} = \Sigma_{i=1}^{n}(a_{i}X^{i}-b_{i}Y^{i})$

Does the average primeness of natural numbers tend to zero?

Generations of a counting sequence

sum of the first $n^2$ natural numbers closed form

An apparently harmless exercise concerning induction

Are there $2^{\aleph_{0} }$ sets of natural numbers such that each two have finite intersection

Generalised Divisibility

Proof of equivalence between two methods of binary to decimal conversion.

Prove that when writing up all even numbers in a column, then chaining $2n+1$ from them, we get all natural numbers exactly once.

Show that a number $n$ is divisible by 6 if and only if it can be written as a sum of three distinct divisors.

Is it true that $n \leq 2^{n-1}$ for all natural numbers $n > 0$?

In Non-standard analysis, is the number of natural numbers a hyperreal number?

Properties of this notion of density in $\Bbb{N}$?

General Solution of Linear Diophantine Equation with 2 and more than 2 variable

Quadratic equation with natural number coefficients

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