List questions from congruences

Published on 11 May 2015 - 2:19

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How to solve congruence modulo equations?

Published on 11 May 2015 - 8:13

1.6k

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Show the congruence $x^{p-1}\equiv 1\pmod{p}$ has $p-1$ solutions

Published on 11 May 2015 - 10:07

160

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Use Gauss' Lemma to find Legendre symbol $\left(\frac{-1}{n}\right)$ for $n \equiv 1, 3, 5, 7 \pmod 8$.

Published on 25 Mar 2026 - 23:42

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Solving to find the general equation with a "mod" equation

Published on 25 Mar 2026 - 19:02

570

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Cubic Congruence Solutions

Published on 13 May 2015 - 21:37

359

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Equality symbols in modular arithmetic

Published on 14 May 2015 - 10:01

987

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Find the remainder when $3^{89}7^{86}$ is divided by $17$

Published on 14 May 2015 - 21:02

57

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Let $n \in \Bbb N$. Find the inverse of $n \pmod {n + 1}$

Published on 17 May 2015 - 18:49

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Solve $x^{2}\equiv 24 \mod 125$

Published on 18 May 2015 - 11:30

120

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Let $m = 4^n+1$ for some integer $n \geqslant 1.$ Prove that $3^{(m-1)/2} \equiv -1 \pmod m$ if and only if $m$ is prime.

Published on 18 May 2015 - 21:27

552

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Solving the congruence $3x^2 + 6x + 1 \equiv 0 \pmod {19}$

Published on 22 Mar 2026 - 15:31

3.1k

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Describe all odd primes p for which 7 is a quadratic residue

Published on 25 Mar 2026 - 19:25

58

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Simple Congruence Problem

Published on 19 May 2015 - 22:11

463

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Prove that $ax \equiv 1 \bmod n \implies \gcd(a,n) = 1$.

Published on 20 May 2015 - 9:26

List Question

Consider $n, k ∈ \mathbb{N}$. Prove that $\gcd(n, n + k)\mid k$

How to solve congruence modulo equations?

Show the congruence $x^{p-1}\equiv 1\pmod{p}$ has $p-1$ solutions

Use Gauss' Lemma to find Legendre symbol $\left(\frac{-1}{n}\right)$ for $n \equiv 1, 3, 5, 7 \pmod 8$.

Solving to find the general equation with a "mod" equation

Cubic Congruence Solutions

Equality symbols in modular arithmetic

Find the remainder when $3^{89}7^{86}$ is divided by $17$

Let $n \in \Bbb N$. Find the inverse of $n \pmod {n + 1}$

Solve $x^{2}\equiv 24 \mod 125$

Let $m = 4^n+1$ for some integer $n \geqslant 1.$ Prove that $3^{(m-1)/2} \equiv -1 \pmod m$ if and only if $m$ is prime.

Solving the congruence $3x^2 + 6x + 1 \equiv 0 \pmod {19}$

Describe all odd primes p for which 7 is a quadratic residue

Simple Congruence Problem

Prove that $ax \equiv 1 \bmod n \implies \gcd(a,n) = 1$.

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