Question

Let $a$ and $b$ be nonnegative integers. prove that $\gcd(2^a-1,2^b-1)=2^{\gcd(a,b)}-1$

score 175 · Answer 1 · 2017-12-03 04:23:20

175

Views

Let $a$ and $b$ be nonnegative integers. prove that $\gcd(2^a-1,2^b-1)=2^{\gcd(a,b)}-1$

Published on 03 Dec 2017 - 4:23

score 299 · Answer 2 · 2026-02-24 12:01:27

299

Views

Compute the number of ordered pairs of positive integers (a,b) such that the lcm of a and b is $3^35^711^{13}$.

Published on 24 Feb 2026 - 12:01

score 441 · Answer 3 · 2017-12-03 21:15:41

441

Views

Showing $\gcd(p,q)d \mid \gcd(pd,qd)$ and $\gcd(pd,qd)\mid \gcd(p,q)d$ for $\mathbb{Z}$ or $K\left [ X \right ]$

Published on 03 Dec 2017 - 21:15

score 46 · Answer 4 · 2026-03-31 06:44:07

46

Views

Proving the $\gcd$ is divided by $p-1$

Published on 31 Mar 2026 - 6:44

score 1.7k · Answer 5 · 2026-02-24 12:01:28

1.7k

Views

The greatest common divisor of two positive integers less than 100 is equal to 3. Their least common multiple is twelve times one of the integers.

Published on 24 Feb 2026 - 12:01

score 689 · Answer 6 · 2026-02-23 08:41:31

689

Views

Prove that if $q | 2^{p} - 1$ then $q \mid 2^{q-1} - 1$ and $q = 1+2kp$

Published on 23 Feb 2026 - 8:41

score 73 · Answer 7 · 2026-02-24 11:58:04

73

Views

Prove that if $LCM(a,b) = GCF(a,b)^2$, then $b = a^2$

Published on 24 Feb 2026 - 11:58

score 127 · Answer 8 · 2026-03-29 03:35:39

127

Views

Common factors of $f, \lambda g$ when $\lambda \in R$, $f,g \in R[x]$ have only constant common factors.

Published on 29 Mar 2026 - 3:35

score 603 · Answer 9 · 2017-12-07 08:41:11

603

Views

$\gcd(a,b)$ is the least positive linear combination of $a$ and $b$

Published on 07 Dec 2017 - 8:41

score 108 · Answer 10 · 2026-03-27 02:21:46

108

Views

Prove that $gcd(G_b,b)=1$

Published on 27 Mar 2026 - 2:21

score 169 · Answer 11 · 2017-12-08 21:23:49

169

Views

if $\frac{a}{b}$ divides $\frac{c}{d}$, and $gcd(a,b)=gcd(c,d)=1,$ then does $b = d$?

Published on 08 Dec 2017 - 21:23

score 72 · Answer 12 · 2017-12-09 06:33:29

72

Views

Finding significance of equalities involved in proving $\gcd(a,b) = \gcd(a{'}, b{'})$.

Published on 09 Dec 2017 - 6:33

score 960 · Answer 13 · 2017-12-09 08:20:50

960

Views

Minimum number of operations required to make GCD equal to K

Published on 09 Dec 2017 - 8:20

score 1k · Answer 14 · 2017-12-10 08:50:45

1k

Views

Suppose that $a, m$ and $n$ are positive integers such that $(m, n)=1$. If $m\mid a$ and $n\mid a$, then $mn\mid a$.

Published on 10 Dec 2017 - 8:50

score 34 · Answer 15 · 2017-12-10 20:33:21

34

Views

Buying items in a nation with only two types of dollar bills?

Published on 10 Dec 2017 - 20:33

List Question

Let $a$ and $b$ be nonnegative integers. prove that $\gcd(2^a-1,2^b-1)=2^{\gcd(a,b)}-1$

Compute the number of ordered pairs of positive integers (a,b) such that the lcm of a and b is $3^35^711^{13}$.

Showing $\gcd(p,q)d \mid \gcd(pd,qd)$ and $\gcd(pd,qd)\mid \gcd(p,q)d$ for $\mathbb{Z}$ or $K\left [ X \right ]$

Proving the $\gcd$ is divided by $p-1$

The greatest common divisor of two positive integers less than 100 is equal to 3. Their least common multiple is twelve times one of the integers.

Prove that if $q | 2^{p} - 1$ then $q \mid 2^{q-1} - 1$ and $q = 1+2kp$

Prove that if $LCM(a,b) = GCF(a,b)^2$, then $b = a^2$

Common factors of $f, \lambda g$ when $\lambda \in R$, $f,g \in R[x]$ have only constant common factors.

$\gcd(a,b)$ is the least positive linear combination of $a$ and $b$

Prove that $gcd(G_b,b)=1$

if $\frac{a}{b}$ divides $\frac{c}{d}$, and $gcd(a,b)=gcd(c,d)=1,$ then does $b = d$?

Finding significance of equalities involved in proving $\gcd(a,b) = \gcd(a{'}, b{'})$.

Minimum number of operations required to make GCD equal to K

Suppose that $a, m$ and $n$ are positive integers such that $(m, n)=1$. If $m\mid a$ and $n\mid a$, then $mn\mid a$.

Buying items in a nation with only two types of dollar bills?

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