Question

Using Euclidean Algorithm to find GCD of polynomials in $\mathbb{Q}[x]$

score 1k · Answer 1 · 2026-03-28 20:13:03

1k

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Using Euclidean Algorithm to find GCD of polynomials in $\mathbb{Q}[x]$

Published on 28 Mar 2026 - 20:13

score 1.7k · Answer 2 · 2026-04-01 22:37:23

1.7k

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If $ab$ is a square number and $\gcd(a,b) = 1$, then $a$ and $b$ are square numbers.

Published on 01 Apr 2026 - 22:37

score 91 · Answer 3 · 2026-03-28 20:14:11

91

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Let $k \in \mathbb{Z}^+$. Use the Euclidean Algorithm to compute $gcd(7k+14; 3k+6)$.

Published on 28 Mar 2026 - 20:14

score 70 · Answer 4 · 2017-04-27 04:48:49

70

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Find all postive $m$ such $\gcd(m,2n!+1)=1,\forall n\in N^{+}$

Published on 27 Apr 2017 - 4:48

score 1k · Answer 5 · 2017-04-27 17:30:15

1k

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Prove that among any five consecutive positive integers there is one integer which is relatively prime to the other four integers.

Published on 27 Apr 2017 - 17:30

score 350 · Answer 6 · 2017-04-30 00:33:22

350

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Show that $\textrm{ker}(p(\phi ))=0$ if and only if the greatest common divisor of $p$ and $m_{\phi }:=m_{M(\phi )}$ is $1$.

Published on 30 Apr 2017 - 0:33

score 55 · Answer 7 · 2026-03-29 20:51:51

55

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Bezout-like equation for coprime $f,g \in F[x]$ where $F$ is a field

Published on 29 Mar 2026 - 20:51

score 491 · Answer 8 · 2017-05-01 22:10:22

491

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gcd of two monic polynomials

Published on 01 May 2017 - 22:10

score 132 · Answer 9 · 2017-05-02 01:25:52

132

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Prove that if $\forall \ i\neq j \in \{1,...,k\}$, $\gcd(n_i,n_j)=1$ then $\gcd(n_1,...,n_k)=1$

Published on 02 May 2017 - 1:25

score 302 · Answer 10 · 2026-04-02 21:52:15

302

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Find the number of common, odd positive divisors of 27, 900 & 20, 700.

Published on 02 Apr 2026 - 21:52

score 51 · Answer 11 · 2017-05-03 05:47:33

51

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Seeking explanation for a curious reciprocity-like identity.

Published on 03 May 2017 - 5:47

score 4.9k · Answer 12 · 2017-05-03 21:16:22

4.9k

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Is the product of two coprime numbers coprime with a third if the three numbers are pairwise coprime?

Published on 03 May 2017 - 21:16

score 96 · Answer 13 · 2017-05-07 07:43:27

96

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Prove that $\gcd(F_{n+1},F_n)$ takes exactly $n-1$ iteration steps for computation.

Published on 07 May 2017 - 7:43

score 281 · Answer 14 · 2017-05-07 13:52:38

281

Views

Bezout's identity in finite fields

Published on 07 May 2017 - 13:52

score 157 · Answer 15 · 2026-03-28 12:39:16

157

Views

Lattice points on a line y = -x + p visible from the origin

Published on 28 Mar 2026 - 12:39

List Question

Using Euclidean Algorithm to find GCD of polynomials in $\mathbb{Q}[x]$

If $ab$ is a square number and $\gcd(a,b) = 1$, then $a$ and $b$ are square numbers.

Let $k \in \mathbb{Z}^+$. Use the Euclidean Algorithm to compute $gcd(7k+14; 3k+6)$.

Find all postive $m$ such $\gcd(m,2n!+1)=1,\forall n\in N^{+}$

Prove that among any five consecutive positive integers there is one integer which is relatively prime to the other four integers.

Show that $\textrm{ker}(p(\phi ))=0$ if and only if the greatest common divisor of $p$ and $m_{\phi }:=m_{M(\phi )}$ is $1$.

Bezout-like equation for coprime $f,g \in F[x]$ where $F$ is a field

gcd of two monic polynomials

Prove that if $\forall \ i\neq j \in \{1,...,k\}$, $\gcd(n_i,n_j)=1$ then $\gcd(n_1,...,n_k)=1$

Find the number of common, odd positive divisors of 27, 900 & 20, 700.

Seeking explanation for a curious reciprocity-like identity.

Is the product of two coprime numbers coprime with a third if the three numbers are pairwise coprime?

Prove that $\gcd(F_{n+1},F_n)$ takes exactly $n-1$ iteration steps for computation.

Bezout's identity in finite fields

Lattice points on a line y = -x + p visible from the origin

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