Question

Prove that gcd(a, b) divides a−b.

score 1.4k · Answer 1 · 2026-04-29 12:52:18

1.4k

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Prove that gcd(a, b) divides a−b.

Published on 29 Apr 2026 - 12:52

score 92 · Answer 2 · 2026-04-29 12:51:39

92

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Measure exactly $n$ gallons of water using 9- and 15- gallon jugs...

Published on 29 Apr 2026 - 12:51

score 43 · Answer 3 · 2026-04-29 12:52:19

43

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What is $|\{n\in N:n\mid p^2q\}|$?

Published on 29 Apr 2026 - 12:52

score 323 · Answer 4 · 2026-05-06 17:25:42

323

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Bivariate polynomials coprime implies finitely many common roots

Published on 06 May 2026 - 17:25

score 1.7k · Answer 5 · 2026-04-29 12:52:20

1.7k

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$ \gcd(x^n-1,x^m-1)=x^d-1$

Published on 29 Apr 2026 - 12:52

score 75 · Answer 6 · 2026-04-29 12:51:39

75

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What does it meant :$4$ and $2(1+\sqrt{5}))$ without Great commone divisor?

Published on 29 Apr 2026 - 12:51

score 327 · Answer 7 · 2026-04-29 12:52:03

327

Views

Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = \gcd(a,b)$

Published on 29 Apr 2026 - 12:52

score 609 · Answer 8 · 2026-03-24 22:07:37

609

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Suppose $\gcd(a,b)=1$ and $c|ab$. Prove there exist integers $r$ and $s$ such that $c=rs, r|a, s|b$, and $\gcd(r,s)=1$

Published on 24 Mar 2026 - 22:07

score 140 · Answer 9 · 2026-04-29 12:52:15

140

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If $c \mid a, c \mid b$ and $d = \gcd(a, b)$, then $\gcd(\frac{a}{c},\frac{b}{c}) = \frac{d}{c}$.

Published on 29 Apr 2026 - 12:52

score 60 · Answer 10 · 2026-04-29 12:51:34

60

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Prove that any positive integer that divides both $c-a$ and $c+a$ must be equal to 1 or 2

Published on 29 Apr 2026 - 12:51

score 42 · Answer 11 · 2026-04-29 12:52:06

42

Views

Elementary Number Theory - question maybe using modular arithmetic

Published on 29 Apr 2026 - 12:52

score 103 · Answer 12 · 2026-04-29 12:51:38

103

Views

Confirmation of Proof: $\gcd(k,b) \Rightarrow \gcd(ka,b) = \gcd(a,b)$

Published on 29 Apr 2026 - 12:51

score 420 · Answer 13 · 2026-04-29 12:51:42

420

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Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$

Published on 29 Apr 2026 - 12:51

score 91 · Answer 14 · 2026-04-29 12:51:36

91

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Prove that $hxyz$ is a perfect square.

Published on 29 Apr 2026 - 12:51

score 113 · Answer 15 · 2026-04-29 12:52:06

113

Views

Number theory Proof on GCD

Published on 29 Apr 2026 - 12:52

List Question

Prove that gcd(a, b) divides a−b.

Measure exactly $n$ gallons of water using 9- and 15- gallon jugs...

What is $|\{n\in N:n\mid p^2q\}|$?

Bivariate polynomials coprime implies finitely many common roots

$ \gcd(x^n-1,x^m-1)=x^d-1$

What does it meant :$4$ and $2(1+\sqrt{5}))$ without Great commone divisor?

Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = \gcd(a,b)$

Suppose $\gcd(a,b)=1$ and $c|ab$. Prove there exist integers $r$ and $s$ such that $c=rs, r|a, s|b$, and $\gcd(r,s)=1$

If $c \mid a, c \mid b$ and $d = \gcd(a, b)$, then $\gcd(\frac{a}{c},\frac{b}{c}) = \frac{d}{c}$.

Prove that any positive integer that divides both $c-a$ and $c+a$ must be equal to 1 or 2

Elementary Number Theory - question maybe using modular arithmetic

Confirmation of Proof: $\gcd(k,b) \Rightarrow \gcd(ka,b) = \gcd(a,b)$

Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$

Prove that $hxyz$ is a perfect square.

Number theory Proof on GCD

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