List questions from congruences

Published on 10 Mar 2017 - 5:48

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Congruence of variable x, y and z

Published on 10 Mar 2017 - 6:13

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Prove that $b_n = b_{n+100}$

Published on 10 Mar 2017 - 22:16

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Given an odd prime $p$, prove that $2(p - 3)!$ is congruent to $-1 \bmod p$

Published on 13 Mar 2017 - 17:39

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Solve a system of two congruences with modules not pairwise coprime

Published on 15 Mar 2017 - 0:05

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Solve the congruence $10^{n+1} - 9n - 10 \equiv 0$ (mod 7)

Published on 15 Mar 2017 - 1:44

358

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Congruence Modulo Powers of Primes

Published on 15 Mar 2017 - 19:07

44

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For which primes $p$ can one always find $q$ such that $X^2+(pq-1)Y^2 \equiv 0\!\pmod{p^2}$ has no solution?

Published on 15 Mar 2017 - 19:33

31

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simultaneous linear congruences question

Published on 15 Mar 2017 - 23:25

60

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Confused as to why $x^2 \equiv 1 \pmod p$ has at most 2 solutions when $p$ is an odd prime

Published on 16 Mar 2017 - 6:48

735

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How to show that the square of an integer$\equiv 0,1,-1\pmod 5$?

Published on 18 Mar 2017 - 10:18

49

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Number of solutions of that congruence?

Published on 18 Mar 2017 - 10:42

26

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Primitive root modulo $p$.

Published on 18 Mar 2017 - 13:12

401

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Prove $\binom{2p+1}{p}\equiv2$ mod $p$ when $p$ is any prime.

Published on 19 Mar 2017 - 15:06

383

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Division by $p$ mod $p$

Published on 19 Mar 2017 - 16:46

List Question

If $a$ has exponent $h$ mod $p$, and $h$ is even, then $a^{h/2} \equiv -1 \bmod p$

Congruence of variable x, y and z

Prove that $b_n = b_{n+100}$

Given an odd prime $p$, prove that $2(p - 3)!$ is congruent to $-1 \bmod p$

Solve a system of two congruences with modules not pairwise coprime

Solve the congruence $10^{n+1} - 9n - 10 \equiv 0$ (mod 7)

Congruence Modulo Powers of Primes

For which primes $p$ can one always find $q$ such that $X^2+(pq-1)Y^2 \equiv 0\!\pmod{p^2}$ has no solution?

simultaneous linear congruences question

Confused as to why $x^2 \equiv 1 \pmod p$ has at most 2 solutions when $p$ is an odd prime

How to show that the square of an integer$\equiv 0,1,-1\pmod 5$?

Number of solutions of that congruence?

Primitive root modulo $p$.

Prove $\binom{2p+1}{p}\equiv2$ mod $p$ when $p$ is any prime.

Division by $p$ mod $p$

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