Question

Given two nonzero integers $a$ and $b$, what can be said about their common divisor based on the following equation?

score 199 · Answer 1 · 2019-11-07 02:12:09

199

Views

Given two nonzero integers $a$ and $b$, what can be said about their common divisor based on the following equation?

Published on 07 Nov 2019 - 2:12

score 477 · Answer 2 · 2019-11-07 03:50:42

477

Views

Prove the divisibility test by $7,11,13$ for numbers more than six digits

Published on 07 Nov 2019 - 3:50

score 144 · Answer 3 · 2019-11-07 07:32:22

144

Views

Find natural number $x=523...$ ($6$ digits) such that :$\begin{cases}x\equiv 0\pmod{7}\\x\equiv 0\pmod{8}\\x\equiv 0\pmod{9}\end{cases}$

Published on 07 Nov 2019 - 7:32

score 63 · Answer 4 · 2019-11-07 08:04:39

63

Views

$a_{n}$ geometric sequence, prove that : $a_{1}+a_{2}+a_{3}+...+a_{n}\|\ a_{1}^{k}+a_{2}^{k}+a_{2}^{k}+...+a_{n}^{k}$ with $(n,k)=1$

Published on 07 Nov 2019 - 8:04

score 36 · Answer 5 · 2019-11-09 10:00:57

36

Views

Prove that $\forall n \in \mathbb{N}, n \ge 2 \Rightarrow n \nmid (2^n-1)$.

Published on 09 Nov 2019 - 10:00

score 264 · Answer 6 · 2026-03-26 06:19:57

264

Views

Using the WOP to check divisibility

Published on 26 Mar 2026 - 6:19

score 255 · Answer 7 · 2019-11-10 17:44:01

255

Views

Determine all prime numbers $p,q,r$ such that : $p^{2}+1=r^{2}+q^{2}$

Published on 10 Nov 2019 - 17:44

score 182 · Answer 8 · 2026-02-23 06:37:58

182

Views

Coprimality of certain linear combinations of Fibonacci numbers (integer coefficients)

Published on 23 Feb 2026 - 6:37

score 1.8k · Answer 9 · 2019-11-10 20:34:04

1.8k

Views

Is "If a | bc, then a | b or a | c" valid?

Published on 10 Nov 2019 - 20:34

score 599 · Answer 10 · 2019-11-11 03:30:19

599

Views

Proving $364 \mid n^{91} - n^7$ [Generalization of Euler & Fermat Theorems]

Published on 11 Nov 2019 - 3:30

score 1.5k · Answer 11 · 2019-11-11 08:44:11

1.5k

Views

Why should the sign of remainder be same as dividend?

Published on 11 Nov 2019 - 8:44

score 56 · Answer 12 · 2019-11-11 08:54:28

56

Views

Ways to prove a * b ^ g(n) + c * d ^ h(n) is divisible by e

Published on 11 Nov 2019 - 8:54

score 132 · Answer 13 · 2026-03-29 08:15:14

132

Views

Find all $n$ natural numbers such that : $n^{2}-3$ divisible by a perfect square $m>1$

Published on 29 Mar 2026 - 8:15

score 114 · Answer 14 · 2026-03-27 01:13:37

114

Views

Wilson's Theorem Lemma

Published on 27 Mar 2026 - 1:13

score 5k · Answer 15 · 2026-03-28 09:34:22

5k

Views

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

Published on 28 Mar 2026 - 9:34

List Question

Given two nonzero integers $a$ and $b$, what can be said about their common divisor based on the following equation?

Prove the divisibility test by $7,11,13$ for numbers more than six digits

Find natural number $x=523...$ ($6$ digits) such that :$\begin{cases}x\equiv 0\pmod{7}\\x\equiv 0\pmod{8}\\x\equiv 0\pmod{9}\end{cases}$

$a_{n}$ geometric sequence, prove that : $a_{1}+a_{2}+a_{3}+...+a_{n}\|\ a_{1}^{k}+a_{2}^{k}+a_{2}^{k}+...+a_{n}^{k}$ with $(n,k)=1$

Prove that $\forall n \in \mathbb{N}, n \ge 2 \Rightarrow n \nmid (2^n-1)$.

Using the WOP to check divisibility

Determine all prime numbers $p,q,r$ such that : $p^{2}+1=r^{2}+q^{2}$

Coprimality of certain linear combinations of Fibonacci numbers (integer coefficients)

Is "If a | bc, then a | b or a | c" valid?

Proving $364 \mid n^{91} - n^7$ [Generalization of Euler & Fermat Theorems]

Why should the sign of remainder be same as dividend?

Ways to prove a * b ^ g(n) + c * d ^ h(n) is divisible by e

Find all $n$ natural numbers such that : $n^{2}-3$ divisible by a perfect square $m>1$

Wilson's Theorem Lemma

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

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