Question

Find $\gcd(a,b)$ knowing that $(a^3+6b^2,6480)=216$ and $11a+8b \mid 540$

score 205 · Answer 1 · 2026-03-27 03:43:17

205

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Find $\gcd(a,b)$ knowing that $(a^3+6b^2,6480)=216$ and $11a+8b \mid 540$

Published on 27 Mar 2026 - 3:43

score 49 · Answer 2 · 2016-10-05 22:27:35

49

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Relative primes proof

Published on 05 Oct 2016 - 22:27

score 135 · Answer 3 · 2026-03-30 00:05:23

135

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What is the probability that the GCD of $n$ naturals $\le m$ is 1?

Published on 30 Mar 2026 - 0:05

score 95 · Answer 4 · 2016-10-08 12:34:36

95

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Elementary Number Theory : a property about gcd

Published on 08 Oct 2016 - 12:34

score 620 · Answer 5 · 2026-03-29 12:39:21

620

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Show that exist infinitely many pairs of natural numbers $(m, n)$ such that $\text{gcd}(m^2+1, n^2+1)=m+n$.

Published on 29 Mar 2026 - 12:39

score 324 · Answer 6 · 2026-03-24 21:10:31

324

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Find three distinct positive integers $x,y,z$ such that $15xyz=\text{lcm}(x,y,z)\cdot \gcd(x,y,z)$

Published on 24 Mar 2026 - 21:10

score 573 · Answer 7 · 2016-10-09 08:30:49

573

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Proof about divisibility and greatest common divisor that doesn't use Bezout's formula

Published on 09 Oct 2016 - 8:30

score 280 · Answer 8 · 2016-10-09 21:58:56

280

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Why do $g'|g$ and $g|g'$, when $g=\gcd(a,b)$ and $g'=\gcd(a,b)$?

Published on 09 Oct 2016 - 21:58

score 113 · Answer 9 · 2016-10-10 11:26:39

113

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$\gcd(a_n ,a_{n+k})< \frac{a_k}2$ for a sequence such that $a_{k+2}=a_{k+1}+a_k$ and $\gcd(a_1,a_2)=1$

Published on 10 Oct 2016 - 11:26

score 981 · Answer 10 · 2026-03-27 05:36:16

981

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GCD and congruence proof

Published on 27 Mar 2026 - 5:36

score 45 · Answer 11 · 2016-10-13 15:17:34

45

Views

If $\gcd(A, B) = 1$, what sufficient condition(s) (if any) guarantee $\gcd(A, C) = \gcd(B, C) = 1$?

Published on 13 Oct 2016 - 15:17

score 2.6k · Answer 12 · 2026-03-25 15:59:03

2.6k

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How can I find $\gcd(16+7i,10-5i)$ by using the Euclidean algorithm?

Published on 25 Mar 2026 - 15:59

score 944 · Answer 13 · 2016-10-17 02:28:17

944

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Proof of $\gcd(n!+1, (n+1)!+1)=1$?

Published on 17 Oct 2016 - 2:28

score 490 · Answer 14 · 2016-10-18 17:22:39

490

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Proof of this property of greatest common divisor: $\gcd( n! + 1 , (n+1)! + 1 ) = 1$

Published on 18 Oct 2016 - 17:22

score 2.6k · Answer 15 · 2016-10-19 07:59:35

2.6k

Views

prime numbers and greatest common divisor

Published on 19 Oct 2016 - 7:59

List Question

Find $\gcd(a,b)$ knowing that $(a^3+6b^2,6480)=216$ and $11a+8b \mid 540$

Relative primes proof

What is the probability that the GCD of $n$ naturals $\le m$ is 1?

Elementary Number Theory : a property about gcd

Show that exist infinitely many pairs of natural numbers $(m, n)$ such that $\text{gcd}(m^2+1, n^2+1)=m+n$.

Find three distinct positive integers $x,y,z$ such that $15xyz=\text{lcm}(x,y,z)\cdot \gcd(x,y,z)$

Proof about divisibility and greatest common divisor that doesn't use Bezout's formula

Why do $g'|g$ and $g|g'$, when $g=\gcd(a,b)$ and $g'=\gcd(a,b)$?

$\gcd(a_n ,a_{n+k})< \frac{a_k}2$ for a sequence such that $a_{k+2}=a_{k+1}+a_k$ and $\gcd(a_1,a_2)=1$

GCD and congruence proof

If $\gcd(A, B) = 1$, what sufficient condition(s) (if any) guarantee $\gcd(A, C) = \gcd(B, C) = 1$?

How can I find $\gcd(16+7i,10-5i)$ by using the Euclidean algorithm?

Proof of $\gcd(n!+1, (n+1)!+1)=1$?

Proof of this property of greatest common divisor: $\gcd( n! + 1 , (n+1)! + 1 ) = 1$

prime numbers and greatest common divisor

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