List questions from congruences

Published on 26 Mar 2026 - 7:58

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If $(a,n)=1$, prove that $ax \equiv b \mod n$ has exactly one solution $t$ such that $0\leq t < n$.

Published on 25 Mar 2016 - 3:55

534

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Proving if $2^n + n^2$ is a prime, show that $n ≡ 3 \pmod 6$

Published on 25 Mar 2016 - 17:26

253

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What is $\prod_{k=1}^{(p-1)/2} (2k-1)^2 \bmod p$ where $p$ is an odd prime?

Published on 27 Mar 2016 - 7:06

1.4k

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Does the method of substitution always work for solving linear congruence systems?

Published on 30 Mar 2026 - 16:04

168

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Find smallest x so that 13^k ≡ x (mod 100)

Published on 28 Mar 2016 - 23:10

1.1k

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Broken Clock vs Normal Clock

Published on 29 Mar 2016 - 0:51

647

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Prove that if $n\neq 2 \pmod 4$ then there exists a primitive Pythagorean triple $(x,y,z)$ in which $x$ or $y$ equals $n$

Published on 25 Mar 2026 - 17:21

227

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Determine if each coefficient of polynomial is congruent to $0$ modulo $p$

Published on 30 Mar 2016 - 8:36

985

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Primitive roots generated from a primitive root

Published on 23 Feb 2026 - 15:12

230

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Is $every$ prime factor of $\frac{n^{163}-1}{n-1}$ either $163$ or $1\;\text{mod}\;163$?

Published on 02 Apr 2016 - 19:12

1.2k

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An integer sequence defined by recursion

Published on 04 Apr 2016 - 4:02

747

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How to solve the congruence $y^{31}\equiv 3 \mod{100}$

Published on 05 Apr 2016 - 21:22

650

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Determine a matrix given two other matrices

Published on 06 Apr 2016 - 10:54

73

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For which positive exponents $e$ is $2^e \equiv 1\pmod{17}$?

Published on 07 Apr 2016 - 17:48

List Question

Using Hensel's Lemma to find the number of solutions.

If $(a,n)=1$, prove that $ax \equiv b \mod n$ has exactly one solution $t$ such that $0\leq t < n$.

Proving if $2^n + n^2$ is a prime, show that $n ≡ 3 \pmod 6$

What is $\prod_{k=1}^{(p-1)/2} (2k-1)^2 \bmod p$ where $p$ is an odd prime?

Does the method of substitution always work for solving linear congruence systems?

Find smallest x so that 13^k ≡ x (mod 100)

Broken Clock vs Normal Clock

Prove that if $n\neq 2 \pmod 4$ then there exists a primitive Pythagorean triple $(x,y,z)$ in which $x$ or $y$ equals $n$

Determine if each coefficient of polynomial is congruent to $0$ modulo $p$

Primitive roots generated from a primitive root

Is $every$ prime factor of $\frac{n^{163}-1}{n-1}$ either $163$ or $1\;\text{mod}\;163$?

An integer sequence defined by recursion

How to solve the congruence $y^{31}\equiv 3 \mod{100}$

Determine a matrix given two other matrices

For which positive exponents $e$ is $2^e \equiv 1\pmod{17}$?

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