List questions from congruences

Published on 05 Mar 2015 - 2:39

259

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Is there a primality test based on the sum of squares of the first $n$ natural numbers $\sum_{x = 1}^{n} x^2$?

Published on 27 Mar 2026 - 0:10

273

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How to show $n^5 + 29 n$ is divisible by $30$

Published on 07 Mar 2015 - 23:14

130

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Congruence of square-free numbers

Published on 08 Mar 2015 - 16:14

150

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Find all the $16^{th}$ roots of $2 \bmod 178481$

Published on 08 Mar 2015 - 18:21

423

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Proof involving gcd and congruence.

Published on 08 Mar 2015 - 18:25

146

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Prove congruence using Fermat's Little Theorem

Published on 08 Mar 2015 - 18:41

113

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Proof with congruence and primes. $(p\mid a^2+b^2)(p\not\mid a,p\not\mid b)\implies \exists c\in\mathbb Z( c^2=-1\pmod {p})$.

Published on 08 Mar 2015 - 18:47

76

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Prove that $x^4\:\equiv\:-4\bmod\:p\:\iff\:p\equiv1\bmod\:4$

Published on 10 Mar 2015 - 4:13

48

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if $p \mid (a^2 + b^2 )$, $p \nmid a$ and $p \nmid b$. Prove that there exists an integer $c$ such that $c^2 \equiv −1 \mod p$.

Published on 11 Mar 2015 - 8:24

698

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A prime number generator algorithm based on $x^2+(x-1)^2$ that generates only primes

Published on 11 Mar 2015 - 9:44

15.2k

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How to solve a congruence system?

Published on 12 Mar 2015 - 6:52

136

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How to solve a quintic congruence equation?

Published on 13 Mar 2015 - 2:26

929

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How to solve polynomial Congruence

Published on 14 Mar 2015 - 15:33

33

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If $(N,M)=N$ and $(k,2N)=1$, does there exist $m\equiv k \pmod{2N}$ such that $(m,M)=1$?

Published on 14 Mar 2015 - 21:49

List Question

Using Wilson's Theorem

Is there a primality test based on the sum of squares of the first $n$ natural numbers $\sum_{x = 1}^{n} x^2$?

How to show $n^5 + 29 n$ is divisible by $30$

Congruence of square-free numbers

Find all the $16^{th}$ roots of $2 \bmod 178481$

Proof involving gcd and congruence.

Prove congruence using Fermat's Little Theorem

Proof with congruence and primes. $(p\mid a^2+b^2)(p\not\mid a,p\not\mid b)\implies \exists c\in\mathbb Z( c^2=-1\pmod {p})$.

Prove that $x^4\:\equiv\:-4\bmod\:p\:\iff\:p\equiv1\bmod\:4$

if $p \mid (a^2 + b^2 )$, $p \nmid a$ and $p \nmid b$. Prove that there exists an integer $c$ such that $c^2 \equiv −1 \mod p$.

A prime number generator algorithm based on $x^2+(x-1)^2$ that generates only primes

How to solve a congruence system?

How to solve a quintic congruence equation?

How to solve polynomial Congruence

If $(N,M)=N$ and $(k,2N)=1$, does there exist $m\equiv k \pmod{2N}$ such that $(m,M)=1$?

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