List questions from congruence-relations

Published on 14 Apr 2026 - 20:10

157

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If $\lambda\subseteq\mathscr{L}, \rho\subseteq\mathscr{R}$, then $\lambda\circ\rho=\rho\circ\lambda$.

Published on 15 Apr 2026 - 12:09

83

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Show that $4(p-5)! + 1 \equiv 0 \pmod p$

Published on 25 Mar 2026 - 7:43

30

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Find $a$ inverse modulo 30, $1\le a \le 30$. For each $a$ you find, find the inverse of each $a$ that have inverse modulo 30

Published on 25 Mar 2026 - 7:45

303

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"Self-congruent" matrices examples

Published on 01 Apr 2026 - 15:36

151

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How to solve a non-linear system of modulus equations?

Published on 06 May 2026 - 6:20

131

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Prove/Disprove that the following relation is a congruence relation

Published on 25 Mar 2026 - 6:04

757

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Proving that if gcd(a,n)=gcd(b,n)=1, then ax+by = c (modn) has exactly n different solutions mod n.

Published on 25 Mar 2026 - 6:04

94

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$n\bar k=\overline{nk}$ in $Z_m$?

Published on 01 Apr 2026 - 15:37

106

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Integer Factor Congruence

Published on 01 Apr 2026 - 3:02

92

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$k-$th root modulo $n$.

Published on 26 Apr 2026 - 8:25

29

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Congruence on semigroup

Published on 31 Mar 2026 - 23:59

74

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How can we obtain $\sum_{l=1}^{m}(-1)^{l+1} \binom{m}{l} \equiv 1\pmod{p}$

Published on 25 Mar 2026 - 6:06

118

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Prove that if $p$ is prime, then an element of $\mathbb{Z} /p \mathbb{Z}$ has at most two square roots.

Published on 25 Mar 2026 - 6:04

69

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Is 7($11^{106}$)+290 divisible by 13?

Published on 25 Mar 2026 - 6:02

List Question

Proof: Every normal subgroup has corresponding Congruence relation and vice versa

If $\lambda\subseteq\mathscr{L}, \rho\subseteq\mathscr{R}$, then $\lambda\circ\rho=\rho\circ\lambda$.

Show that $4(p-5)! + 1 \equiv 0 \pmod p$

Find $a$ inverse modulo 30, $1\le a \le 30$. For each $a$ you find, find the inverse of each $a$ that have inverse modulo 30

"Self-congruent" matrices examples

How to solve a non-linear system of modulus equations?

Prove/Disprove that the following relation is a congruence relation

Proving that if gcd(a,n)=gcd(b,n)=1, then ax+by = c (modn) has exactly n different solutions mod n.

$n\bar k=\overline{nk}$ in $Z_m$?

Integer Factor Congruence

$k-$th root modulo $n$.

Congruence on semigroup

How can we obtain $\sum_{l=1}^{m}(-1)^{l+1} \binom{m}{l} \equiv 1\pmod{p}$

Prove that if $p$ is prime, then an element of $\mathbb{Z} /p \mathbb{Z}$ has at most two square roots.

Is 7($11^{106}$)+290 divisible by 13?

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