Question

Composite integers and Wilson's theorem in a problem

score 196 · Answer 1 · 2026-04-12 02:15:17

196

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Composite integers and Wilson's theorem in a problem

Published on 12 Apr 2026 - 2:15

score 865 · Answer 2 · 2026-04-13 15:14:48

865

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What is the probability of that a number in the set of natural numbers is divisible by $3$ but not by $9$?

Published on 13 Apr 2026 - 15:14

score 488 · Answer 3 · 2026-04-16 00:37:40

488

Views

Prove that if $3\mid n$ and $5\mid n$, then $15\mid n$

Published on 16 Apr 2026 - 0:37

score 155 · Answer 4 · 2026-05-10 13:44:58

155

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Proof involving Euler totient function

Published on 10 May 2026 - 13:44

score 724 · Answer 5 · 2026-04-15 19:43:02

724

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$6$ digit numbers formed from the first six positive integers such that they are divisible by both $4$ and $3$.

Published on 15 Apr 2026 - 19:43

score 182 · Answer 6 · 2026-05-10 20:38:12

182

Views

Why does the method for division work?

Published on 10 May 2026 - 20:38

score 87 · Answer 7 · 2026-04-16 11:11:45

87

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$\frac{dx}{u}=\frac{dt}{1}=\frac{du}{0}\iff\frac{u}{dx}=\frac{1}{dt}=\frac{0}{du}$?

Published on 16 Apr 2026 - 11:11

score 229 · Answer 8 · 2026-05-10 12:32:39

229

Views

Why multiplying by base b works when converting fractions from one base to another?

Published on 10 May 2026 - 12:32

score 2.2k · Answer 9 · 2026-04-14 15:07:26

2.2k

Views

A problem on divisibility: If $c$ divides $ab$ and $\gcd(b,c)=1$, then prove that $c$ divides $a$.

Published on 14 Apr 2026 - 15:07

score 158 · Answer 10 · 2026-04-16 00:09:57

158

Views

$N$ is divisible by $5$ iff $a_0=0$ or $5$

Published on 16 Apr 2026 - 0:09

score 190 · Answer 11 · 2026-05-10 15:03:08

190

Views

We have $a^{n-1} \equiv 1\ (mod\ n)$ but $a^{m} \not\equiv 1\ (mod\ n)$ for every divisor $m$ of $n - 1$, other than itself. Prove that $n$ is prime.

Published on 10 May 2026 - 15:03

score 39 · Answer 12 · 2026-04-17 13:06:18

39

Views

To find a short way to prove - if $p$ is a prime and $p|a^2+b^2, \space p|b^2+c^2$, then $p|a, p|b, p|a^2-c^2$

Published on 17 Apr 2026 - 13:06

score 144 · Answer 13 · 2026-04-12 10:29:39

144

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A problem from a mathematical olympiad

Published on 12 Apr 2026 - 10:29

score 48 · Answer 14 · 2026-04-14 13:31:30

48

Views

Proof by divisibility. Should I choose $a=p$ and $b=p^2$?

Published on 14 Apr 2026 - 13:31

score 28 · Answer 15 · 2026-04-11 12:33:39

28

Views

Proof check (Divisibility)

Published on 11 Apr 2026 - 12:33

List Question

Composite integers and Wilson's theorem in a problem

What is the probability of that a number in the set of natural numbers is divisible by $3$ but not by $9$?

Prove that if $3\mid n$ and $5\mid n$, then $15\mid n$

Proof involving Euler totient function

$6$ digit numbers formed from the first six positive integers such that they are divisible by both $4$ and $3$.

Why does the method for division work?

$\frac{dx}{u}=\frac{dt}{1}=\frac{du}{0}\iff\frac{u}{dx}=\frac{1}{dt}=\frac{0}{du}$?

Why multiplying by base b works when converting fractions from one base to another?

A problem on divisibility: If $c$ divides $ab$ and $\gcd(b,c)=1$, then prove that $c$ divides $a$.

$N$ is divisible by $5$ iff $a_0=0$ or $5$

We have $a^{n-1} \equiv 1\ (mod\ n)$ but $a^{m} \not\equiv 1\ (mod\ n)$ for every divisor $m$ of $n - 1$, other than itself. Prove that $n$ is prime.

To find a short way to prove - if $p$ is a prime and $p|a^2+b^2, \space p|b^2+c^2$, then $p|a, p|b, p|a^2-c^2$

A problem from a mathematical olympiad

Proof by divisibility. Should I choose $a=p$ and $b=p^2$?

Proof check (Divisibility)

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