List questions from gcd-and-lcm

Published on 11 Nov 2015 - 7:45

76

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Prove that $(a+b, a-b) \ge (a, b)$

Published on 11 Nov 2015 - 11:16

89

Views

Congruence equation of 2 unknown numbers

Published on 30 Mar 2026 - 10:38

63

Views

If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$

Published on 12 Nov 2015 - 5:55

113

Views

Abstract algebra - UFDs

Published on 29 Mar 2026 - 12:45

370

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Large sum of 1/GCD's

Published on 30 Mar 2026 - 17:08

1.1k

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If $(a,b)=1$ and $n$ is a prime, prove that $(a^n+b^n)/(a+b)$ and $(a+b)$ have no common factor, unless $a+b$ is a multiple of $n$

Published on 13 Nov 2015 - 11:55

747

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If $p$ is prime and $\gcd(m,p) = 1$ show that $\gcd(m,p^k) = 1$

Published on 14 Nov 2015 - 18:45

697

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Euler's totient function and related sum

Published on 29 Mar 2026 - 12:23

145

Views

Why is $\gcd(2^p + 1,3^p + 1) = 1$?

Published on 27 Mar 2026 - 1:48

80

Views

Proof $\gcd(a, 18) = \gcd(a + 18,\gcd(a, 18))$

Published on 16 Nov 2015 - 18:02

49

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Why do we say that $gcd (a,b) \le gcd(a, b-a)$

Published on 19 Nov 2015 - 20:43

541

Views

Proving relatively prime using GCD definition

Published on 20 Nov 2015 - 3:03

96

Views

greatest common divisor proof

Published on 20 Nov 2015 - 9:06

320

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Prove that $\gcd(ab,m) \mid ( \gcd(a,m) *\ gcd(b,m) )$

Published on 20 Nov 2015 - 13:58

List Question

least common multiple of $\{1,2,...,n\}$ is bigger than $2^{n-1}$

Prove that $(a+b, a-b) \ge (a, b)$

Congruence equation of 2 unknown numbers

If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$

Abstract algebra - UFDs

Large sum of 1/GCD's

If $(a,b)=1$ and $n$ is a prime, prove that $(a^n+b^n)/(a+b)$ and $(a+b)$ have no common factor, unless $a+b$ is a multiple of $n$

If $p$ is prime and $\gcd(m,p) = 1$ show that $\gcd(m,p^k) = 1$

Euler's totient function and related sum

Why is $\gcd(2^p + 1,3^p + 1) = 1$?

Proof $\gcd(a, 18) = \gcd(a + 18,\gcd(a, 18))$

Why do we say that $gcd (a,b) \le gcd(a, b-a)$

Proving relatively prime using GCD definition

greatest common divisor proof

Prove that $\gcd(ab,m) \mid ( \gcd(a,m) *\ gcd(b,m) )$

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