Question

Find the smallest natural number $n$ such that every $n$-element subset of $S=\{1,2,\dots,280\}$ contains $5$ pairwise relatively prime numbers

score 1.6k · Answer 1 · 2021-11-03 15:20:08

1.6k

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Find the smallest natural number $n$ such that every $n$-element subset of $S=\{1,2,\dots,280\}$ contains $5$ pairwise relatively prime numbers

Published on 03 Nov 2021 - 15:20

score 71 · Answer 2 · 2021-11-14 19:44:25

71

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Rank of a pair of coprime integers

Published on 14 Nov 2021 - 19:44

score 42 · Answer 3 · 2021-12-02 22:42:21

42

Views

Property of coprime integer.

Published on 02 Dec 2021 - 22:42

score 94 · Answer 4 · 2021-12-04 08:26:25

94

Views

Find the smallest natural number k such that between k different and in pairs relatively prime natural numbers less than 2021 there's a prime number

Published on 04 Dec 2021 - 8:26

score 34 · Answer 5 · 2021-12-25 07:48:42

34

Views

Prove that the set $A(d)=\{m\in\mathbb{Z}|1\leq m\leq n\quad\&\quad gcd(m,n)=d\}$ are pairwise disjoint

Published on 25 Dec 2021 - 7:48

score 39 · Answer 6 · 2022-03-24 11:17:01

39

Views

Lower bound on number of integers in interval which are coprime to every other integer on interval

Published on 24 Mar 2022 - 11:17

score 73 · Answer 7 · 2022-04-01 08:23:10

73

Views

How to prove that the number 6+2 can be represented as the sum of two coprime numbers?

Published on 01 Apr 2022 - 8:23

score 395 · Answer 8 · 2022-04-13 13:25:48

395

Views

Show that for all $n$, If $n$ is a multiple of $58$, then $n+7$ and $n^{2}+9$ are coprime.

Published on 13 Apr 2022 - 13:25

score 435 · Answer 9 · 2022-04-20 21:35:26

435

Views

No infinite arithmetic progression exists with prime numbers

Published on 20 Apr 2022 - 21:35

score 207 · Answer 10 · 2022-04-24 00:10:59

207

Views

Conjecture: Every $n \geq 20 \in \mathbb{N}$ can be written as a sum of three integers $(\geq 2)$ that are pairwise coprime

Published on 24 Apr 2022 - 0:10

score 54 · Answer 11 · 2022-05-06 18:55:06

54

Views

Expressing any even natural number as a sum of primorials with coefficients

Published on 06 May 2022 - 18:55

score 204 · Answer 12 · 2022-05-13 01:07:16

204

Views

PHI function to list relative primes

Published on 13 May 2022 - 1:07

score 150 · Answer 13 · 2022-05-25 13:43:23

150

Views

Equivalent integral quadratic forms properly represent the same integers

Published on 25 May 2022 - 13:43

score 218 · Answer 14 · 2022-06-03 20:31:26

218

Views

Infinite numbers of coprime pairs $k(6k-1)$.

Published on 03 Jun 2022 - 20:31

score 64 · Answer 15 · 2022-06-29 20:25:57

64

Views

Coprime with $n$ and their modular inverses in $\Bbb Z_n$

Published on 29 Jun 2022 - 20:25

List Question

Find the smallest natural number $n$ such that every $n$-element subset of $S=\{1,2,\dots,280\}$ contains $5$ pairwise relatively prime numbers

Rank of a pair of coprime integers

Property of coprime integer.

Find the smallest natural number k such that between k different and in pairs relatively prime natural numbers less than 2021 there's a prime number

Prove that the set $A(d)=\{m\in\mathbb{Z}|1\leq m\leq n\quad\&\quad gcd(m,n)=d\}$ are pairwise disjoint

Lower bound on number of integers in interval which are coprime to every other integer on interval

How to prove that the number 6+2 can be represented as the sum of two coprime numbers?

Show that for all $n$, If $n$ is a multiple of $58$, then $n+7$ and $n^{2}+9$ are coprime.

No infinite arithmetic progression exists with prime numbers

Conjecture: Every $n \geq 20 \in \mathbb{N}$ can be written as a sum of three integers $(\geq 2)$ that are pairwise coprime

Expressing any even natural number as a sum of primorials with coefficients

PHI function to list relative primes

Equivalent integral quadratic forms properly represent the same integers

Infinite numbers of coprime pairs $k(6k-1)$.

Coprime with $n$ and their modular inverses in $\Bbb Z_n$

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