Question

If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]

score 2.6k · Answer 1 · 2015-04-01 19:15:26

2.6k

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If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]

Published on 01 Apr 2015 - 19:15

score 1.4k · Answer 2 · 2015-04-01 23:56:46

1.4k

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Determining maximum possible number of pieces of a bar with given number of cuts

Published on 01 Apr 2015 - 23:56

score 246 · Answer 3 · 2026-04-10 23:28:37

246

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Greatest integer which divides $2001\times\ 2002\times 2003\times\ \cdots\times\ 2009$

Published on 10 Apr 2026 - 23:28

score 1.8k · Answer 4 · 2026-03-29 11:02:09

1.8k

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Proof that $(2^m - 1, 2^n - 1) = 2^d - 1$ where $d = (m,n)$

Published on 29 Mar 2026 - 11:02

score 58 · Answer 5 · 2015-04-02 17:05:21

58

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$m+n = (n,m)^2; n+l = (n,l)^2; l+m = (m,l)^2$

Published on 02 Apr 2015 - 17:05

score 340 · Answer 6 · 2026-04-07 09:29:52

340

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Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction

Published on 07 Apr 2026 - 9:29

score 84 · Answer 7 · 2026-03-25 19:05:01

84

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Prove that $\{ ax+by\mid x,y\in\mathbb Z\} = \{ n(a,b) \mid n\in\mathbb Z\}$

Published on 25 Mar 2026 - 19:05

score 115 · Answer 8 · 2015-04-04 13:34:45

115

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If $n$ is a positive integer such that $2^n+n^2$ is a prime number , then is it true that $6|n-3$ ?

Published on 04 Apr 2015 - 13:34

score 13.6k · Answer 9 · 2015-04-05 23:14:09

13.6k

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Why is the sum of the digits in a multiple of 9 also a multiple of 9?

Published on 05 Apr 2015 - 23:14

score 43 · Answer 10 · 2015-04-05 23:21:03

43

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A question related to the concept of being "relatively prime"

Published on 05 Apr 2015 - 23:21

score 72 · Answer 11 · 2026-03-26 16:56:49

72

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On odd perfect numbers $N$ given in the Eulerian form $N = {q^k}{n^2}$, Part II

Published on 26 Mar 2026 - 16:56

score 136 · Answer 12 · 2026-04-02 17:46:06

136

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Let $k = (a+b,a^2+b^2-ab)$. If $(a,b)=1$ then $k = 1$ or $k=3$.

Published on 02 Apr 2026 - 17:46

score 55 · Answer 13 · 2015-04-07 20:53:40

55

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Existence of non-coprime between an integer and an arithmetic sequence

Published on 07 Apr 2015 - 20:53

score 221 · Answer 14 · 2026-04-10 17:39:11

221

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Prove if $7\mid a^2+b^2 \longrightarrow 7\mid a$ and $ 7\mid b$

Published on 10 Apr 2026 - 17:39

score 939 · Answer 15 · 2015-04-08 20:42:28

939

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Odd divisibility induction proof

Published on 08 Apr 2015 - 20:42

List Question

If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]

Determining maximum possible number of pieces of a bar with given number of cuts

Greatest integer which divides $2001\times\ 2002\times 2003\times\ \cdots\times\ 2009$

Proof that $(2^m - 1, 2^n - 1) = 2^d - 1$ where $d = (m,n)$

$m+n = (n,m)^2; n+l = (n,l)^2; l+m = (m,l)^2$

Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction

Prove that $\{ ax+by\mid x,y\in\mathbb Z\} = \{ n(a,b) \mid n\in\mathbb Z\}$

If $n$ is a positive integer such that $2^n+n^2$ is a prime number , then is it true that $6|n-3$ ?

Why is the sum of the digits in a multiple of 9 also a multiple of 9?

A question related to the concept of being "relatively prime"

On odd perfect numbers $N$ given in the Eulerian form $N = {q^k}{n^2}$, Part II

Let $k = (a+b,a^2+b^2-ab)$. If $(a,b)=1$ then $k = 1$ or $k=3$.

Existence of non-coprime between an integer and an arithmetic sequence

Prove if $7\mid a^2+b^2 \longrightarrow 7\mid a$ and $ 7\mid b$

Odd divisibility induction proof

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