List questions from congruences

Published on 25 Feb 2016 - 7:49

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Is there a solution for $x^6 \equiv 5 \pmod {71}$?

Published on 23 Feb 2026 - 10:02

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When is $991n^2 +1$ a perfect square?

Published on 26 Feb 2016 - 12:00

398

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If $p$ is an odd prime and $p \nmid a$, show that $a^{(p-1)/2} \equiv \pm 1 \pmod {p}$

Published on 25 Mar 2026 - 12:28

60

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Congruence modulo $n$ problem

Published on 28 Feb 2016 - 17:04

182

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If a prime $p>2$ is expressible as $p=a^2+b^2$, then $4\mid (p-1)$

Published on 28 Mar 2026 - 19:30

37

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What can be said about the smallest $N$ where $N^2 \not\equiv 1$ mod $p_x$; for all $x : 1 \leq x \leq y$

Published on 28 Mar 2026 - 19:39

186

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Use the Chinese Remainder Theorem to find the smallest element of a set

Published on 30 Mar 2026 - 14:11

64

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Simultaneous congruences to different moduli

Published on 02 Mar 2016 - 13:52

367

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Proof quadratic congruent equation has no solutions in $\mathbb{N}$

Published on 02 Mar 2016 - 14:12

178

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Bernoulli Number Congruence

Published on 27 Mar 2026 - 2:39

109

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Find all solutions of the equation $x^2+x=0$ in $\mathbb Z_6$

Published on 02 Mar 2016 - 21:08

718

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Prove that if $p$ is an odd prime and $x$ is an integer such that $x^2\equiv 1~mod~p^k$, then $x=\pm 1~mod~p^k$

Published on 02 Mar 2016 - 23:45

1.5k

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A problem on chinese remainder theorem (CSIR NET DEC 2015)

Published on 30 Mar 2026 - 14:16

222

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Method to Solve Linear Congruences

Published on 03 Mar 2016 - 19:19

List Question

How to solve these two simultaneous "divisibilities" : $n+1\mid m^2+1$ and $m+1\mid n^2+1$

Is there a solution for $x^6 \equiv 5 \pmod {71}$?

When is $991n^2 +1$ a perfect square?

If $p$ is an odd prime and $p \nmid a$, show that $a^{(p-1)/2} \equiv \pm 1 \pmod {p}$

Congruence modulo $n$ problem

If a prime $p>2$ is expressible as $p=a^2+b^2$, then $4\mid (p-1)$

What can be said about the smallest $N$ where $N^2 \not\equiv 1$ mod $p_x$; for all $x : 1 \leq x \leq y$

Use the Chinese Remainder Theorem to find the smallest element of a set

Simultaneous congruences to different moduli

Proof quadratic congruent equation has no solutions in $\mathbb{N}$

Bernoulli Number Congruence

Find all solutions of the equation $x^2+x=0$ in $\mathbb Z_6$

Prove that if $p$ is an odd prime and $x$ is an integer such that $x^2\equiv 1~mod~p^k$, then $x=\pm 1~mod~p^k$

A problem on chinese remainder theorem (CSIR NET DEC 2015)

Method to Solve Linear Congruences

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