Question

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

score 68 · Answer 1 · 2018-04-15 17:33:40

68

Views

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

Published on 15 Apr 2018 - 17:33

score 248 · Answer 2 · 2026-03-25 11:10:13

248

Views

Congruence involving Bernoulli numbers

Published on 25 Mar 2026 - 11:10

score 56 · Answer 3 · 2018-04-18 01:19:56

56

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 18 Apr 2018 - 1:19

score 186 · Answer 4 · 2018-04-20 13:30:53

186

Views

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

Published on 20 Apr 2018 - 13:30

score 110 · Answer 5 · 2018-04-23 15:32:04

110

Views

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

Published on 23 Apr 2018 - 15:32

score 433 · Answer 6 · 2018-04-29 16:01:59

433

Views

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

Published on 29 Apr 2018 - 16:01

score 1k · Answer 7 · 2014-03-12 02:25:49

1k

Views

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

Published on 12 Mar 2014 - 2:25

score 504 · Answer 8 · 2014-03-12 08:49:13

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 · 2014-03-12 14:28:42

1.5k

Views

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

Published on 12 Mar 2014 - 14:28

score 1k · Answer 10 · 2014-03-12 13:59:28

1k

Views

Solution of cubic modulo some prime

Published on 12 Mar 2014 - 13:59

score 298 · Answer 11 · 2014-03-12 22:33:10

298

Views

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

Published on 12 Mar 2014 - 22:33

score 263 · Answer 12 · 2014-03-16 17:15:59

263

Views

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

Published on 16 Mar 2014 - 17:15

score 25 · Answer 13 · 2014-03-16 17:40:22

25

Views

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

Published on 16 Mar 2014 - 17:40

score 228 · Answer 14 · 2014-03-17 02:37:20

228

Views

Simple Congruence Question Using Fermat's Little Theorem

Published on 17 Mar 2014 - 2:37

score 92 · Answer 15 · 2014-03-17 16:27:07

92

Views

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

Published on 17 Mar 2014 - 16:27

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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