List questions from congruences

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number theory polynomial congruences

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How to solve linear congruences as a newbie?

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Show for prime numbers of the form $p=4n+1$, $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.

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Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$

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Solve congruence: $45x \equiv 15 \pmod{78}$ (What am I doing wrong?)

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Divisibility rules and congruences

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Use congruences to show that $6$ divides $n^3 – n$ for every integer $n$

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244

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Euler, Fermat and primes

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Why is $a^n - b^n$ divisible by $a-b$?

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$n\mid \phi(a^{n}-1)$ for any $a>n$?

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Solving a non-linear congruence

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Prove: $a\equiv b\pmod{n} \implies \gcd(a,n)=\gcd(b,n)$

Published on 28 Feb 2013 - 17:15

108

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How to find the remainder $x^y\bmod z$ quickly?

Published on 26 Mar 2013 - 18:19

List Question

$2^p -1$ then $p$ is a prime

number theory polynomial congruences

How to solve linear congruences as a newbie?

Show for prime numbers of the form $p=4n+1$, $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.

Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$

Solve congruence: $45x \equiv 15 \pmod{78}$ (What am I doing wrong?)

Divisibility rules and congruences

Use congruences to show that $6$ divides $n^3 – n$ for every integer $n$

Euler, Fermat and primes

Why is $a^n - b^n$ divisible by $a-b$?

$n\mid \phi(a^{n}-1)$ for any $a>n$?

Solving a non-linear congruence

Prove: $a\equiv b\pmod{n} \implies \gcd(a,n)=\gcd(b,n)$

How to find the remainder $x^y\bmod z$ quickly?

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