List questions from gcd-and-lcm

Published on 25 Apr 2026 - 12:20

38

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Number Theory: Divisibilty

Published on 09 Apr 2026 - 5:26

319

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$\gcd(a,b)=1 \iff \gcd(a+b,ab)=1$.

Published on 15 Apr 2026 - 12:32

293

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Determine the greatest common divisor of polynomials $x^2+1$ and $x^3+1$ in $\Bbb Q[X]$.

Published on 16 Apr 2026 - 18:48

623

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Modular inverse of Gaussian Integers

Published on 10 May 2026 - 11:20

439

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Prove that $gcd \left(2^{x}-1, 2^{y}-1\right) = 2^{gcd(x,y)}-1$

Published on 16 Apr 2026 - 16:15

155

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Prove that $\gcd(a+s,b+s)=1$ for infinitely many numbers $s$

Published on 14 Apr 2026 - 20:22

71

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GCD of successive terms

Published on 09 Apr 2026 - 5:42

51

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Find the value of a if A divisable by 3

Published on 09 Apr 2026 - 5:28

114

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Finding the correct $x$ to $ax - by = 1$

Published on 10 May 2026 - 18:01

53

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Prove that if $\\gcd(a,b)=1$ then $a\mathbb{N}\cap b\mathbb{N}=(ab)\mathbb{N}.$

Published on 16 Apr 2026 - 8:38

558

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Consider the equation $a_n +b_n\sqrt{2} = (1+\sqrt{2})^n$ where $a_n, b_n \in \mathbb{Z} \ge 1$. Prove that $\gcd(a_n, b_n) = 1$.

Published on 16 Apr 2026 - 0:49

72

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GCD as integral operator

Published on 11 Apr 2026 - 13:37

249

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Let $ab=cd$ and $\gcd(a,c)=1$. Then $a | d$ and $c | b$.

Published on 15 Apr 2026 - 20:37

134

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Greatest Common Divisor in a Diophantine Equation

Published on 14 Apr 2026 - 7:12

List Question

Organizing objects in a near-square pattern

Number Theory: Divisibilty

$\gcd(a,b)=1 \iff \gcd(a+b,ab)=1$.

Determine the greatest common divisor of polynomials $x^2+1$ and $x^3+1$ in $\Bbb Q[X]$.

Modular inverse of Gaussian Integers

Prove that $gcd \left(2^{x}-1, 2^{y}-1\right) = 2^{gcd(x,y)}-1$

Prove that $\gcd(a+s,b+s)=1$ for infinitely many numbers $s$

GCD of successive terms

Find the value of a if A divisable by 3

Finding the correct $x$ to $ax - by = 1$

Prove that if $\\gcd(a,b)=1$ then $a\mathbb{N}\cap b\mathbb{N}=(ab)\mathbb{N}.$

Consider the equation $a_n +b_n\sqrt{2} = (1+\sqrt{2})^n$ where $a_n, b_n \in \mathbb{Z} \ge 1$. Prove that $\gcd(a_n, b_n) = 1$.

GCD as integral operator

Let $ab=cd$ and $\gcd(a,c)=1$. Then $a | d$ and $c | b$.

Greatest Common Divisor in a Diophantine Equation

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