Question

How can I show that $x \equiv b^{u} \pmod m$ is always a solution to $x^{k} \equiv \pmod m$, even if $\gcd(b,m) \gt 1$?

score 255 · Answer 1 · 2015-10-02 15:21:29

255

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How can I show that $x \equiv b^{u} \pmod m$ is always a solution to $x^{k} \equiv \pmod m$, even if $\gcd(b,m) \gt 1$?

Published on 02 Oct 2015 - 15:21

score 228 · Answer 2 · 2015-10-02 19:04:42

228

Views

gcd and lcm triples

Published on 02 Oct 2015 - 19:04

score 79 · Answer 3 · 2015-10-03 10:11:42

79

Views

Finding X and Y for given equation

Published on 03 Oct 2015 - 10:11

score 1.9k · Answer 4 · 2015-10-03 23:03:39

1.9k

Views

GCD induction proof

Published on 03 Oct 2015 - 23:03

score 1.3k · Answer 5 · 2015-10-04 15:18:10

1.3k

Views

Prove $\gcd\left(\frac{a^m - 1}{a -1},a -1\right) = \gcd(m,a-1)$

Published on 04 Oct 2015 - 15:18

score 183 · Answer 6 · 2015-10-04 15:36:57

183

Views

If $\gcd(m,n)=1$, then $\gcd(2^m+1,2^n+1)\in\{1,3\}$

Published on 04 Oct 2015 - 15:36

score 397 · Answer 7 · 2015-10-06 01:34:17

397

Views

Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.

Published on 06 Oct 2015 - 1:34

score 2.8k · Answer 8 · 2015-10-06 05:43:48

2.8k

Views

Set of numbers with no common factor that has max sum

Published on 06 Oct 2015 - 5:43

score 146 · Answer 9 · 2015-10-07 05:40:36

146

Views

Is there a way to show that $\gcd(a,b) = ax + by $ without also showing that its the smallest positive linear combination?

Published on 07 Oct 2015 - 5:40

score 149 · Answer 10 · 2015-10-07 15:16:52

149

Views

How do you show if $d \mid a$ and $d \mid b$ then $d \mid \gcd(a,b)$ without knowing that $\gcd(a,b)$ is a linear combination of $a$ and $b$?

Published on 07 Oct 2015 - 15:16

score 1k · Answer 11 · 2026-02-24 02:15:02

1k

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If a divisor of $pq-1$ divides the LCM of $p-1$ and $q-1$, then it also divides the GCD of these two numbers

Published on 24 Feb 2026 - 2:15

score 986 · Answer 12 · 2015-10-08 02:17:49

986

Views

Prove divisibility with gcd: If $ar+bs=d=\gcd(a,b)$, then $r$ and $s$ are relatively prime

Published on 08 Oct 2015 - 2:17

score 2.4k · Answer 13 · 2015-10-08 19:18:35

2.4k

Views

Relatively Prime Relationship Equation Proof

Published on 08 Oct 2015 - 19:18

score 207 · Answer 14 · 2015-10-09 12:29:51

207

Views

Divisibility of subsets of the set $1, 2, 3, ..., n$

Published on 09 Oct 2015 - 12:29

score 247 · Answer 15 · 2026-03-29 03:10:59

247

Views

Probability that two integers chosen at random from an arithmetic progression are coprime

Published on 29 Mar 2026 - 3:10

List Question

How can I show that $x \equiv b^{u} \pmod m$ is always a solution to $x^{k} \equiv \pmod m$, even if $\gcd(b,m) \gt 1$?

gcd and lcm triples

Finding X and Y for given equation

GCD induction proof

Prove $\gcd\left(\frac{a^m - 1}{a -1},a -1\right) = \gcd(m,a-1)$

If $\gcd(m,n)=1$, then $\gcd(2^m+1,2^n+1)\in\{1,3\}$

Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.

Set of numbers with no common factor that has max sum

Is there a way to show that $\gcd(a,b) = ax + by $ without also showing that its the smallest positive linear combination?

How do you show if $d \mid a$ and $d \mid b$ then $d \mid \gcd(a,b)$ without knowing that $\gcd(a,b)$ is a linear combination of $a$ and $b$?

If a divisor of $pq-1$ divides the LCM of $p-1$ and $q-1$, then it also divides the GCD of these two numbers

Prove divisibility with gcd: If $ar+bs=d=\gcd(a,b)$, then $r$ and $s$ are relatively prime

Relatively Prime Relationship Equation Proof

Divisibility of subsets of the set $1, 2, 3, ..., n$

Probability that two integers chosen at random from an arithmetic progression are coprime

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