Question

Prove that: $(a,b)=p_1^{\delta_1}p_2^{\delta_2}\cdots p_k^{\delta_k}$, where $\delta_i = \min(\alpha_i,\beta_i) \forall i$.

score 32 · Answer 1 · 2022-09-01 16:59:24

32

Views

Prove that: $(a,b)=p_1^{\delta_1}p_2^{\delta_2}\cdots p_k^{\delta_k}$, where $\delta_i = \min(\alpha_i,\beta_i) \forall i$.

Published on 01 Sep 2022 - 16:59

score 90 · Answer 2 · 2022-09-03 08:38:11

90

Views

Does $\gcd(a,b)=\gcd(\left|a\right|,\left|b\right|)$ imply that GCDs are nonnegative?

Published on 03 Sep 2022 - 8:38

score 67 · Answer 3 · 2022-09-05 09:40:59

67

Views

Is it true that $\gcd(\left|a\right|,\left|b\right|) \leq \min(\left|a\right|,\left|b\right|)$, if $ab \neq 0$?

Published on 05 Sep 2022 - 9:40

score 121 · Answer 4 · 2022-09-09 18:03:31

121

Views

Nearest overlapping time for periodic flashing light bulbs

Published on 09 Sep 2022 - 18:03

score 197 · Answer 5 · 2026-04-01 14:25:04

197

Views

Find all $m\ge 2$ such that $\phi(n,m)\ge (m-n)\phi(1,m)/m$ and $m^2\mid 2022^m+1$

Published on 01 Apr 2026 - 14:25

score 47 · Answer 6 · 2026-04-01 09:48:49

47

Views

Prove that there exists such a natural number sequence $a_1,a_2,\ldots$, such that $GCD(a_n,2^{a_n}+1)\rightarrow\infty$ when $n\rightarrow\infty$

Published on 01 Apr 2026 - 9:48

score 221 · Answer 7 · 2022-09-20 17:39:18

221

Views

Prove there exist infinitely many $n\in\mathbb N$ for any $a,b,c\in\mathbb N$ which are distinct such that $a+n,b+n,c+n$ are pairwise coprime

Published on 20 Sep 2022 - 17:39

score 108 · Answer 8 · 2026-04-09 07:18:00

108

Views

How does one find the GCD of three numbers with large exponent values?

Published on 09 Apr 2026 - 7:18

score 280 · Answer 9 · 2026-04-05 17:47:11

280

Views

Generalising $ab=\text{hcf}(a,b)\text{lcm}(a,b)$

Published on 05 Apr 2026 - 17:47

score 140 · Answer 10 · 2022-09-27 15:24:52

140

Views

$ax+by=c$ has unique solution for positive integers

Published on 27 Sep 2022 - 15:24

score 68 · Answer 11 · 2026-03-27 22:53:56

68

Views

Are these valid proofs for the equation $\gcd(n,\sigma(n^2))=\gcd(n^2,\sigma(n^2))$, if $q^k n^2$ is an odd perfect number with special prime $q$?

Published on 27 Mar 2026 - 22:53

score 34 · Answer 12 · 2026-04-01 02:55:04

34

Views

Number of sides of a regular polygon using LCM.

Published on 01 Apr 2026 - 2:55

score 93 · Answer 13 · 2022-10-01 18:22:30

93

Views

prove that there exists $a_{n+1} > a_n$ with $(a_1+\cdots + a_{n+1} )| (a_1^2 +\cdots + a_{n+1}^2)$

Published on 01 Oct 2022 - 18:22

score 204 · Answer 14 · 2026-04-05 17:55:33

204

Views

Conjecture on the prime factorisation of the $\operatorname{lcm}(1,\dots,k) \pm 1$, $k \geq 2$

Published on 05 Apr 2026 - 17:55

score 48 · Answer 15 · 2022-10-10 14:26:00

48

Views

if a is not equal to b prove that GCD$(a+\sqrt2*b, \sqrt2+1)=1$

Published on 10 Oct 2022 - 14:26

List Question

Prove that: $(a,b)=p_1^{\delta_1}p_2^{\delta_2}\cdots p_k^{\delta_k}$, where $\delta_i = \min(\alpha_i,\beta_i) \forall i$.

Does $\gcd(a,b)=\gcd(\left|a\right|,\left|b\right|)$ imply that GCDs are nonnegative?

Is it true that $\gcd(\left|a\right|,\left|b\right|) \leq \min(\left|a\right|,\left|b\right|)$, if $ab \neq 0$?

Nearest overlapping time for periodic flashing light bulbs

Find all $m\ge 2$ such that $\phi(n,m)\ge (m-n)\phi(1,m)/m$ and $m^2\mid 2022^m+1$

Prove that there exists such a natural number sequence $a_1,a_2,\ldots$, such that $GCD(a_n,2^{a_n}+1)\rightarrow\infty$ when $n\rightarrow\infty$

Prove there exist infinitely many $n\in\mathbb N$ for any $a,b,c\in\mathbb N$ which are distinct such that $a+n,b+n,c+n$ are pairwise coprime

How does one find the GCD of three numbers with large exponent values?

Generalising $ab=\text{hcf}(a,b)\text{lcm}(a,b)$

$ax+by=c$ has unique solution for positive integers

Are these valid proofs for the equation $\gcd(n,\sigma(n^2))=\gcd(n^2,\sigma(n^2))$, if $q^k n^2$ is an odd perfect number with special prime $q$?

Number of sides of a regular polygon using LCM.

prove that there exists $a_{n+1} > a_n$ with $(a_1+\cdots + a_{n+1} )| (a_1^2 +\cdots + a_{n+1}^2)$

Conjecture on the prime factorisation of the $\operatorname{lcm}(1,\dots,k) \pm 1$, $k \geq 2$

if a is not equal to b prove that GCD$(a+\sqrt2*b, \sqrt2+1)=1$

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