Question

Prove that if $p$ is a prime number, then $p|n^p-n$

score 273 · Answer 1 · 2018-03-02 03:45:22

273

Views

Prove that if $p$ is a prime number, then $p|n^p-n$

Published on 02 Mar 2018 - 3:45

score 1.2k · Answer 2 · 2026-03-25 03:00:45

1.2k

Views

Is this relation anti-symmetric?

Published on 25 Mar 2026 - 3:00

score 457 · Answer 3 · 2026-03-21 16:43:05

457

Views

Contrapositive when the consequent is a disjunction

Published on 21 Mar 2026 - 16:43

score 84 · Answer 4 · 2018-03-05 11:30:30

84

Views

Explaining a step in a fraction division problem/proof.

Published on 05 Mar 2018 - 11:30

score 152 · Answer 5 · 2026-03-25 03:07:37

152

Views

Prove that $1+20+20^2+20^3+....+20^{21} \equiv 0\bmod 23$

Published on 25 Mar 2026 - 3:07

score 1.7k · Answer 6 · 2018-03-05 19:46:02

1.7k

Views

How to find least positive integer

Published on 05 Mar 2018 - 19:46

score 196 · Answer 7 · 2018-03-07 01:44:49

196

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Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.

Published on 07 Mar 2018 - 1:44

score 260 · Answer 8 · 2026-03-25 04:43:34

260

Views

Assume $m$ divides $n$. Show for any integer $a$, $[a]_m$ is the union of $[a]_n, [a+m]_n, [a+2m]_n,..., [a+(n-m)]_n$

Published on 25 Mar 2026 - 4:43

score 66 · Answer 9 · 2018-03-07 11:37:08

66

Views

If $a|b$, then why the gcd of $a$ and $b$ is $a$?

Published on 07 Mar 2018 - 11:37

score 93 · Answer 10 · 2026-03-25 04:43:27

93

Views

If both sides of $2^{31}\equiv (-1)^{31}\equiv 2\mod 3$ is multiplied by $2$ then will it be $2^{32}\equiv4\mod 3$ or $2^{32}\equiv4\mod 6$?

Published on 25 Mar 2026 - 4:43

score 1k · Answer 11 · 2026-03-25 03:00:51

1k

Views

To find a remainder, when divided by $101$

Published on 25 Mar 2026 - 3:00

score 159 · Answer 12 · 2018-03-08 16:21:27

159

Views

$2^n-1$ is prime or composite as $n$ is prime or composite [without using induction method]

Published on 08 Mar 2018 - 16:21

score 123 · Answer 13 · 2018-03-08 17:23:25

123

Views

Dividers of a number n

Published on 08 Mar 2018 - 17:23

score 2.4k · Answer 14 · 2018-03-08 19:49:03

2.4k

Views

What is the smallest positive integer that is divisible by $2$ and $3$

Published on 08 Mar 2018 - 19:49

score 41 · Answer 15 · 2018-03-08 21:09:50

41

Views

Difference in total number of positive integers $x, y, z$ determined from an equation.

Published on 08 Mar 2018 - 21:09

List Question

Prove that if $p$ is a prime number, then $p|n^p-n$

Is this relation anti-symmetric?

Contrapositive when the consequent is a disjunction

Explaining a step in a fraction division problem/proof.

Prove that $1+20+20^2+20^3+....+20^{21} \equiv 0\bmod 23$

How to find least positive integer

Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.

Assume $m$ divides $n$. Show for any integer $a$, $[a]_m$ is the union of $[a]_n, [a+m]_n, [a+2m]_n,..., [a+(n-m)]_n$

If $a|b$, then why the gcd of $a$ and $b$ is $a$?

If both sides of $2^{31}\equiv (-1)^{31}\equiv 2\mod 3$ is multiplied by $2$ then will it be $2^{32}\equiv4\mod 3$ or $2^{32}\equiv4\mod 6$?

To find a remainder, when divided by $101$

$2^n-1$ is prime or composite as $n$ is prime or composite [without using induction method]

Dividers of a number n

What is the smallest positive integer that is divisible by $2$ and $3$

Difference in total number of positive integers $x, y, z$ determined from an equation.

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