Question

Suppose $x,y,z$ are mutually coprime positive integers that solve $x^2+y^2=z^2$

score 31 · Answer 1 · 2022-04-22 13:31:27

31

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Suppose $x,y,z$ are mutually coprime positive integers that solve $x^2+y^2=z^2$

Published on 22 Apr 2022 - 13:31

score 38 · Answer 2 · 2026-04-01 12:49:15

38

Views

An exact sequence of cyclic groups related to the lcm

Published on 01 Apr 2026 - 12:49

score 314 · Answer 3 · 2022-04-27 05:01:18

314

Views

Approximate LCM (Least Common Multiple) of $n$ random $k$-digit numbers

Published on 27 Apr 2022 - 5:01

score 194 · Answer 4 · 2026-02-23 12:55:47

194

Views

Forming rational numbers using unique Egyptian fractions, all but one of whom have coprime denominators

Published on 23 Feb 2026 - 12:55

score 99 · Answer 5 · 2022-05-06 05:18:30

99

Views

Find the least common multiple of three polynomials

Published on 06 May 2022 - 5:18

score 84 · Answer 6 · 2022-05-07 00:12:29

84

Views

I want $a := mk^2 + mkn$ and $b := mkn + \frac{n^2m}{2}$ to be coprime. That, is I want $\gcd(a, b) = 1$. Which constraints on $m, k, n$ lead to this?

Published on 07 May 2022 - 0:12

score 33 · Answer 7 · 2022-05-07 19:37:36

33

Views

Does $\gcd(a, bc) = 1$ imply $\gcd(a, b) = 1$?

Published on 07 May 2022 - 19:37

score 204 · Answer 8 · 2022-05-17 22:53:01

We are allowed to erase the pair of numbers $(a, b)$ from the board and replace it with one of the following pairs: $(b, a), (a − b, b), (a + b, b)$.

score 316 · Answer 9 · 2022-05-18 21:54:36

316

Views

gcd of $2$ numbers with multiplying on any prime number

Published on 18 May 2022 - 21:54

score 497 · Answer 10 · 2026-03-31 16:24:41

497

Views

To find the maximum possible value of their greatest common divisor $\gcd (a_1,a_2,\cdots, a_7)$.

Published on 31 Mar 2026 - 16:24

score 138 · Answer 11 · 2022-05-21 05:57:50

138

Views

If $ab+1 = r^2$ for $a,b,r \in \mathbb{N},$ how to show that $\gcd(2a(r+b)+1,2b(r+a)+1) = 1?$

Published on 21 May 2022 - 5:57

score 309 · Answer 12 · 2022-05-22 13:20:57

309

Views

Show: $\text{lcm}(a,a+p)=\text{lcm}(b,b+p), p \;\text{prime}\implies a=b$

Published on 22 May 2022 - 13:20

score 140 · Answer 13 · 2026-03-29 16:26:42

140

Views

Divisors in GCD domain

Published on 29 Mar 2026 - 16:26

score 53 · Answer 14 · 2022-05-24 15:07:43

53

Views

Proving that $\alpha\gamma$ and $\beta\gamma$ have no gcd where $\alpha=3$ , $\beta=(1+2\sqrt{-5})$ and $\gamma=7(1+2\sqrt{-5})$in ring $Z[√(-5)]$

Published on 24 May 2022 - 15:07

score 151 · Answer 15 · 2026-02-24 02:16:23

151

Views

Equivalent integral quadratic forms properly represent the same integers

Published on 24 Feb 2026 - 2:16

List Question

Suppose $x,y,z$ are mutually coprime positive integers that solve $x^2+y^2=z^2$

An exact sequence of cyclic groups related to the lcm

Approximate LCM (Least Common Multiple) of $n$ random $k$-digit numbers

Forming rational numbers using unique Egyptian fractions, all but one of whom have coprime denominators

Find the least common multiple of three polynomials

I want $a := mk^2 + mkn$ and $b := mkn + \frac{n^2m}{2}$ to be coprime. That, is I want $\gcd(a, b) = 1$. Which constraints on $m, k, n$ lead to this?

Does $\gcd(a, bc) = 1$ imply $\gcd(a, b) = 1$?

We are allowed to erase the pair of numbers $(a, b)$ from the board and replace it with one of the following pairs: $(b, a), (a − b, b), (a + b, b)$.

gcd of $2$ numbers with multiplying on any prime number

To find the maximum possible value of their greatest common divisor $\gcd (a_1,a_2,\cdots, a_7)$.

If $ab+1 = r^2$ for $a,b,r \in \mathbb{N},$ how to show that $\gcd(2a(r+b)+1,2b(r+a)+1) = 1?$

Show: $\text{lcm}(a,a+p)=\text{lcm}(b,b+p), p \;\text{prime}\implies a=b$

Divisors in GCD domain

Proving that $\alpha\gamma$ and $\beta\gamma$ have no gcd where $\alpha=3$ , $\beta=(1+2\sqrt{-5})$ and $\gamma=7(1+2\sqrt{-5})$in ring $Z[√(-5)]$

Equivalent integral quadratic forms properly represent the same integers

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