Question

What numbers lower than $2016$ are "surprising"?

score 78 · Answer 1 · 2016-10-01 14:53:04

78

Views

What numbers lower than $2016$ are "surprising"?

Published on 01 Oct 2016 - 14:53

score 322 · Answer 2 · 2016-10-08 19:04:53

322

Views

Find three distinct positive integers $x,y,z$ such that $15xyz=\text{lcm}(x,y,z)\cdot \gcd(x,y,z)$

Published on 08 Oct 2016 - 19:04

score 464 · Answer 3 · 2016-10-10 10:05:27

A number is a multiple of $3$ if a sum of all his digits are a multiple of 3. Is it the same thing with multiples of 30?

score 44 · Answer 4 · 2016-10-16 16:19:12

44

Views

Let $p_1,...,p_s$ be a maximal system of irreducible divisors, pairwise non-associated, of $ab$ in a euclidean domain.

Published on 16 Oct 2016 - 16:19

score 68 · Answer 5 · 2016-10-24 02:54:51

68

Views

Prove that $G=\mathbb{Z}_{n_1} \times ... \times \mathbb{Z}_{n_k}$ is cyclic $\iff n_1,...,n_k$ are pairwise coprime

Published on 24 Oct 2016 - 2:54

score 2.7k · Answer 6 · 2016-11-06 16:03:07

2.7k

Views

Finite abelian group contains an element with order equal to the lcm of the orders of its elements

Published on 06 Nov 2016 - 16:03

score 71 · Answer 7 · 2016-11-07 00:29:15

71

Views

Invertible least common multiple matrix

Published on 07 Nov 2016 - 0:29

score 1.3k · Answer 8 · 2016-11-11 17:52:04

1.3k

Views

Prove that you can make change for any amount greater than 7 cents using only 3 and 5 cent coins.

Published on 11 Nov 2016 - 17:52

score 447 · Answer 9 · 2016-11-12 18:30:11

447

Views

Prove $4^m < \operatorname{lcm} (m+1, m+2, \dots, 2m+1)$

Published on 12 Nov 2016 - 18:30

score 74 · Answer 10 · 2016-11-15 10:27:42

74

Views

$\gcd(|H_{1}|,|H_{2}|,\cdots,|H_{n}|) > 1$ implies $H_{1} \times H_{2} \times \cdots \times H_{n} = G$ not cyclic

Published on 15 Nov 2016 - 10:27

score 938 · Answer 11 · 2016-11-19 04:58:41

938

Views

Using of the Least common multiple in the modulo

Published on 19 Nov 2016 - 4:58

score 352 · Answer 12 · 2016-11-22 07:09:16

352

Views

(AIME 1987) Find the number of ordered triples $(a,b,c)$ of positive integers satisfying the following condtions.

Published on 22 Nov 2016 - 7:09

score 196 · Answer 13 · 2016-11-23 10:16:40

196

Views

Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?

Published on 23 Nov 2016 - 10:16

score 1.2k · Answer 14 · 2016-11-30 20:22:47

1.2k

Views

Beginner: How to complete the induction case in a proof that all multiples are a product of the least common multiple

Published on 30 Nov 2016 - 20:22

score 654 · Answer 15 · 2016-12-10 21:38:15

654

Views

Multiplying a floor function

Published on 10 Dec 2016 - 21:38

List Question

What numbers lower than $2016$ are "surprising"?

Find three distinct positive integers $x,y,z$ such that $15xyz=\text{lcm}(x,y,z)\cdot \gcd(x,y,z)$

A number is a multiple of $3$ if a sum of all his digits are a multiple of 3. Is it the same thing with multiples of 30?

Let $p_1,...,p_s$ be a maximal system of irreducible divisors, pairwise non-associated, of $ab$ in a euclidean domain.

Prove that $G=\mathbb{Z}_{n_1} \times ... \times \mathbb{Z}_{n_k}$ is cyclic $\iff n_1,...,n_k$ are pairwise coprime

Finite abelian group contains an element with order equal to the lcm of the orders of its elements

Invertible least common multiple matrix

Prove that you can make change for any amount greater than 7 cents using only 3 and 5 cent coins.

Prove $4^m < \operatorname{lcm} (m+1, m+2, \dots, 2m+1)$

$\gcd(|H_{1}|,|H_{2}|,\cdots,|H_{n}|) > 1$ implies $H_{1} \times H_{2} \times \cdots \times H_{n} = G$ not cyclic

Using of the Least common multiple in the modulo

(AIME 1987) Find the number of ordered triples $(a,b,c)$ of positive integers satisfying the following condtions.

Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?

Beginner: How to complete the induction case in a proof that all multiples are a product of the least common multiple

Multiplying a floor function

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