Question

Chinese Remainder Theorem When GCD is not 1

score 3.8k · Answer 1 · 2026-03-30 17:37:02

3.8k

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Chinese Remainder Theorem When GCD is not 1

Published on 30 Mar 2026 - 17:37

score 3.5k · Answer 2 · 2016-06-03 05:26:21

3.5k

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Prove that if $a$ and $b$ are positive integers satisfying $\gcd(a,b)=\operatorname{lcm}(a,b)$,then $a=b$

Published on 03 Jun 2016 - 5:26

score 229 · Answer 3 · 2026-02-24 05:37:55

229

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Function that turns GCD and LCM into intersections and unions?: $f(a)\cap f(b)=f(\gcd(a,b))$, $f(a)\cup f(b)=f(\operatorname{lcm}(a,b))$

Published on 24 Feb 2026 - 5:37

score 1.1k · Answer 4 · 2016-06-04 17:30:26

1.1k

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How to find a point with positive integer coordinates which is closest to a line?

Published on 04 Jun 2016 - 17:30

score 1.2k · Answer 5 · 2026-03-29 15:29:02

1.2k

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Minimum of $|ax-by+c|$

Published on 29 Mar 2026 - 15:29

score 53 · Answer 6 · 2016-06-06 13:49:12

53

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How to prove that the condition is sufficient?

Published on 06 Jun 2016 - 13:49

score 20 · Answer 7 · 2016-06-06 15:07:02

20

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Find gcd (a:b) with some data

Published on 06 Jun 2016 - 15:07

score 923 · Answer 8 · 2016-06-07 15:58:49

923

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If $(a,b) = 1$ and $ab=c^n$ then $a=x^n$ and $b=y^n$ for some x,y. Proof?

Published on 07 Jun 2016 - 15:58

score 145 · Answer 9 · 2026-03-29 22:31:39

145

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Counting the number of integers in a reduced residue system congruent to some integer modulo a prime

Published on 29 Mar 2026 - 22:31

score 643 · Answer 10 · 2016-06-09 18:57:05

643

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Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$

Published on 09 Jun 2016 - 18:57

score 419 · Answer 11 · 2026-03-30 17:17:22

419

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In an integral domain, if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$

Published on 30 Mar 2026 - 17:17

score 816 · Answer 12 · 2016-06-13 15:43:06

816

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Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$

Published on 13 Jun 2016 - 15:43

score 188 · Answer 13 · 2016-06-13 19:22:11

188

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Prove that $\gcd(3^n-2,2^n-3)=1$ if and only if $\gcd(6^n-4,2^n-3)=1$

Published on 13 Jun 2016 - 19:22

score 2k · Answer 14 · 2016-06-15 12:11:39

2k

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Show that two numbers divided by their GCD are coprime

Published on 15 Jun 2016 - 12:11

score 227 · Answer 15 · 2016-06-17 03:36:36

227

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Upper bound for $\gcd(a,b)$ if $\frac{a+1}{b}+\frac{b+1}{a}\in\Bbb{N}$

Published on 17 Jun 2016 - 3:36

List Question

Chinese Remainder Theorem When GCD is not 1

Prove that if $a$ and $b$ are positive integers satisfying $\gcd(a,b)=\operatorname{lcm}(a,b)$,then $a=b$

Function that turns GCD and LCM into intersections and unions?: $f(a)\cap f(b)=f(\gcd(a,b))$, $f(a)\cup f(b)=f(\operatorname{lcm}(a,b))$

How to find a point with positive integer coordinates which is closest to a line?

Minimum of $|ax-by+c|$

How to prove that the condition is sufficient?

Find gcd (a:b) with some data

If $(a,b) = 1$ and $ab=c^n$ then $a=x^n$ and $b=y^n$ for some x,y. Proof?

Counting the number of integers in a reduced residue system congruent to some integer modulo a prime

Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$

In an integral domain, if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$

Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$

Prove that $\gcd(3^n-2,2^n-3)=1$ if and only if $\gcd(6^n-4,2^n-3)=1$

Show that two numbers divided by their GCD are coprime

Upper bound for $\gcd(a,b)$ if $\frac{a+1}{b}+\frac{b+1}{a}\in\Bbb{N}$

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