Question

Composite integers and Wilson's theorem in a problem

score 193 · Answer 1 · 2018-03-09 14:16:51

193

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Composite integers and Wilson's theorem in a problem

Published on 09 Mar 2018 - 14:16

score 862 · Answer 2 · 2018-03-10 15:57:11

862

Views

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

Published on 10 Mar 2018 - 15:57

score 485 · Answer 3 · 2018-03-12 19:21:59

485

Views

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

Published on 12 Mar 2018 - 19:21

score 151 · Answer 4 · 2026-03-25 06:16:15

151

Views

Proof involving Euler totient function

Published on 25 Mar 2026 - 6:16

score 721 · Answer 5 · 2018-03-14 11:03:15

721

Views

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

Published on 14 Mar 2018 - 11:03

score 174 · Answer 6 · 2026-03-22 16:52:05

174

Views

Why does the method for division work?

Published on 22 Mar 2026 - 16:52

score 84 · Answer 7 · 2018-03-15 04:11:51

84

Views

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

Published on 15 Mar 2018 - 4:11

score 224 · Answer 8 · 2026-03-25 06:02:16

224

Views

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

Published on 25 Mar 2026 - 6:02

score 2.2k · Answer 9 · 2018-03-16 13:15:29

2.2k

Views

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

Published on 16 Mar 2018 - 13:15

score 155 · Answer 10 · 2018-03-17 10:28:34

155

Views

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

Published on 17 Mar 2018 - 10:28

score 188 · Answer 11 · 2018-03-18 20:34:14

188

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 18 Mar 2018 - 20:34

score 36 · Answer 12 · 2018-03-19 08:38:31

36

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 19 Mar 2018 - 8:38

score 141 · Answer 13 · 2018-03-19 11:23:21

141

Views

A problem from a mathematical olympiad

Published on 19 Mar 2018 - 11:23

score 46 · Answer 14 · 2018-03-20 06:48:39

46

Views

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

Published on 20 Mar 2018 - 6:48

score 25 · Answer 15 · 2018-03-20 10:35:27

25

Views

Proof check (Divisibility)

Published on 20 Mar 2018 - 10:35

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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