Question

Maximise $\sum_{x,y\in S} GCD(x,y)$ where $S = \{1,2,\ldots, 100\}$ and each number appears once in the sum

score 93 · Answer 1 · 2026-03-26 09:34:16

93

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Maximise $\sum_{x,y\in S} GCD(x,y)$ where $S = \{1,2,\ldots, 100\}$ and each number appears once in the sum

Published on 26 Mar 2026 - 9:34

score 56 · Answer 2 · 2023-12-22 12:53:46

56

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Given $N = lcm(A,B)+lcm(B,C)+lcm(C,A)$, Prove that N cannot be a power of 2

Published on 22 Dec 2023 - 12:53

score 296 · Answer 3 · 2026-03-29 10:15:18

296

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When are $n!+1$ and $(n+2)!+1$ coprime?

Published on 29 Mar 2026 - 10:15

score 251 · Answer 4 · 2023-12-23 09:05:36

251

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What is the number of ordered triplets of natural numbers $a, b, c$ such that $a b c=2^5 \times 3^7$ and H.C.F. $(a, b, c)=1$

Published on 23 Dec 2023 - 9:05

score 286 · Answer 5 · 2023-12-26 13:57:40

286

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$\text{lcm}(a, b, c) = \frac{ab + bc + ca}4$

Published on 26 Dec 2023 - 13:57

score 88 · Answer 6 · 2023-12-27 13:10:03

Prove by the Gauss lemma that if $a, b \in \mathbb{N} \Rightarrow $ the product $ab$ is equal to the multiplication of $GCD(a;b)$ with $LCM(a;b)$.

score 61 · Answer 7 · 2023-12-30 23:40:48

61

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$a + b$, $b^{p - 1}$ coprime when $a$, $b$ coprime for odd prime $p$

Published on 30 Dec 2023 - 23:40

score 89 · Answer 8 · 2026-02-23 07:55:42

89

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How can I find the periods of difference of the sine waves that has irrational coefficients

Published on 23 Feb 2026 - 7:55

score 30 · Answer 9 · 2024-01-04 20:52:48

30

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Halting condition in modular gcd algorithm

Published on 04 Jan 2024 - 20:52

score 71 · Answer 10 · 2026-03-27 14:57:38

71

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Modeling Nanotubes Geometry

Published on 27 Mar 2026 - 14:57

score 41 · Answer 11 · 2024-01-07 20:15:15

41

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Minimum perimeter of a triangle given certain number of dots on an cartesian plane

Published on 07 Jan 2024 - 20:15

score 77 · Answer 12 · 2024-01-13 13:49:46

Let $a,b,c,d \in\mathbb{Z}^+$. What are the minimal conditions required to state that $LCM(bcd, acd, abd, abc) = abcd$? How could I generalize it?

score 47 · Answer 13 · 2026-04-01 16:07:03

47

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GCD and LCM of n Fractions – Proof of the Formulas

Published on 01 Apr 2026 - 16:07

score 152 · Answer 14 · 2024-01-19 13:38:47

152

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GCD for three numbers (number theory)

Published on 19 Jan 2024 - 13:38

score 108 · Answer 15 · 2024-01-20 17:43:22

108

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smallest child number

Published on 20 Jan 2024 - 17:43

List Question

Maximise $\sum_{x,y\in S} GCD(x,y)$ where $S = \{1,2,\ldots, 100\}$ and each number appears once in the sum

Given $N = lcm(A,B)+lcm(B,C)+lcm(C,A)$, Prove that N cannot be a power of 2

When are $n!+1$ and $(n+2)!+1$ coprime?

What is the number of ordered triplets of natural numbers $a, b, c$ such that $a b c=2^5 \times 3^7$ and H.C.F. $(a, b, c)=1$

$\text{lcm}(a, b, c) = \frac{ab + bc + ca}4$

Prove by the Gauss lemma that if $a, b \in \mathbb{N} \Rightarrow $ the product $ab$ is equal to the multiplication of $GCD(a;b)$ with $LCM(a;b)$.

$a + b$, $b^{p - 1}$ coprime when $a$, $b$ coprime for odd prime $p$

How can I find the periods of difference of the sine waves that has irrational coefficients

Halting condition in modular gcd algorithm

Modeling Nanotubes Geometry

Minimum perimeter of a triangle given certain number of dots on an cartesian plane

Let $a,b,c,d \in\mathbb{Z}^+$. What are the minimal conditions required to state that $LCM(bcd, acd, abd, abc) = abcd$? How could I generalize it?

GCD and LCM of n Fractions – Proof of the Formulas

GCD for three numbers (number theory)

smallest child number

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