Question

Suppose that $a$ is co-prime to $n$. Prove that there exists $z ∈ Z$ such that $az \equiv 1 \pmod n$

score 71 · Answer 1 · 2026-04-16 13:03:59

71

Views

Suppose that $a$ is co-prime to $n$. Prove that there exists $z ∈ Z$ such that $az \equiv 1 \pmod n$

Published on 16 Apr 2026 - 13:03

score 255 · Answer 2 · 2026-05-10 14:52:41

255

Views

Congruence involving Bernoulli numbers

Published on 10 May 2026 - 14:52

score 58 · Answer 3 · 2026-04-15 07:04:35

58

Views

A positive integer $x$ is a solution of the congruence $m^x\equiv 1$ mod $n$ if and only if $ord_nm|x$

Published on 15 Apr 2026 - 7:04

score 189 · Answer 4 · 2026-04-14 19:34:42

189

Views

Prove that $3$ divides $14^{2n}-1$ with modular arithmetic.

Published on 14 Apr 2026 - 19:34

score 114 · Answer 5 · 2026-05-10 13:49:15

114

Views

iff condition for quadratic residue modulo p when $p\equiv3\mod 4$

Published on 10 May 2026 - 13:49

score 436 · Answer 6 · 2026-04-13 18:12:29

436

Views

Trouble Understanding Fermat's Little Theorem for Non-Coprime Case

Published on 13 Apr 2026 - 18:12

score 1k · Answer 7 · 2026-04-14 10:18:26

1k

Views

How can I get the smallest possible answer with the Chinese Remainder Theorem?

Published on 14 Apr 2026 - 10:18

score 507 · Answer 8 · 2026-04-17 01:02:54

If a prime number $p$ satisfies $\gcd(a,p−1) = 1$, then for every integer $b$ the congruence relation $x^a \equiv b \pmod{p}$ has a solution.

score 1.5k · Answer 9 · 2026-04-10 02:27:25

1.5k

Views

What is the difference between Hensel lifting and the Newton-Raphson method?

Published on 10 Apr 2026 - 2:27

score 1k · Answer 10 · 2026-04-15 22:15:27

1k

Views

Solution of cubic modulo some prime

Published on 15 Apr 2026 - 22:15

score 302 · Answer 11 · 2026-05-11 01:08:31

302

Views

Finding all solutions to $3^x \equiv 9 \pmod{13}$

Published on 11 May 2026 - 1:08

score 266 · Answer 12 · 2026-04-17 04:35:37

266

Views

Proving that $mx \equiv 0 \pmod n$ has $\gcd(m, n)$ solutions in the interval $[0, n-1]$

Published on 17 Apr 2026 - 4:35

score 28 · Answer 13 · 2026-04-16 05:13:41

28

Views

How to conclude the congruence $2\cdot \text{disc}(F)\equiv 2b^2c^2\in\mathbb{Z}$

Published on 16 Apr 2026 - 5:13

score 231 · Answer 14 · 2026-04-10 11:15:37

231

Views

Simple Congruence Question Using Fermat's Little Theorem

Published on 10 Apr 2026 - 11:15

score 95 · Answer 15 · 2026-04-16 03:17:03

95

Views

Showing that $(p-2)! \equiv 1 \pmod p$

Published on 16 Apr 2026 - 3:17

List Question

Suppose that $a$ is co-prime to $n$. Prove that there exists $z ∈ Z$ such that $az \equiv 1 \pmod n$

Congruence involving Bernoulli numbers

A positive integer $x$ is a solution of the congruence $m^x\equiv 1$ mod $n$ if and only if $ord_nm|x$

Prove that $3$ divides $14^{2n}-1$ with modular arithmetic.

iff condition for quadratic residue modulo p when $p\equiv3\mod 4$

Trouble Understanding Fermat's Little Theorem for Non-Coprime Case

How can I get the smallest possible answer with the Chinese Remainder Theorem?

If a prime number $p$ satisfies $\gcd(a,p−1) = 1$, then for every integer $b$ the congruence relation $x^a \equiv b \pmod{p}$ has a solution.

What is the difference between Hensel lifting and the Newton-Raphson method?

Solution of cubic modulo some prime

Finding all solutions to $3^x \equiv 9 \pmod{13}$

Proving that $mx \equiv 0 \pmod n$ has $\gcd(m, n)$ solutions in the interval $[0, n-1]$

How to conclude the congruence $2\cdot \text{disc}(F)\equiv 2b^2c^2\in\mathbb{Z}$

Simple Congruence Question Using Fermat's Little Theorem

Showing that $(p-2)! \equiv 1 \pmod p$

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