Question

Show the set of congruence classes mod n is a partition of $\mathbb{Z}$.

score 843 · Answer 1 · 2018-01-11 04:44:09

843

Views

Show the set of congruence classes mod n is a partition of $\mathbb{Z}$.

Published on 11 Jan 2018 - 4:44

score 945 · Answer 2 · 2018-01-13 02:08:56

945

Views

Proof verification: Show that the set of congruence classes form a partition of $\mathbb{Z}$.

Published on 13 Jan 2018 - 2:08

score 1k · Answer 3 · 2012-05-07 20:26:40

1k

Views

Lattices are congruence-distributive

Published on 07 May 2012 - 20:26

score 614 · Answer 4 · 2012-05-25 04:16:18

614

Views

$M_3$ is a simple lattice

Published on 25 May 2012 - 4:16

score 404 · Answer 5 · 2012-08-02 12:35:37

404

Views

CEP for Abelian groups and lattices

Published on 02 Aug 2012 - 12:35

score 1.9k · Answer 6 · 2012-08-03 16:46:55

1.9k

Views

Quotienting a group by an equivalence relation

Published on 03 Aug 2012 - 16:46

score 481 · Answer 7 · 2013-01-25 08:28:20

481

Views

Every group and ring is congruence-permutable , but not necessarily congruence-distributive

Published on 25 Jan 2013 - 8:28

score 177 · Answer 8 · 2013-03-30 03:44:07

177

Views

For a group $G$ and subgroup $H$, is $a \sim b \iff a^{-1}b\in H$ an equivalence relation even when $H$ is not normal?

Published on 30 Mar 2013 - 3:44

score 954 · Answer 9 · 2020-08-05 12:08:06

954

Views

To prove that an operation is well-defined in modular arithmetic

Published on 05 Aug 2020 - 12:08

score 501 · Answer 10 · 2020-08-06 08:25:46

501

Views

$(\forall n \in \mathbb{Z}):n^{3} \equiv n$ (mod $6$)

Published on 06 Aug 2020 - 8:25

score 196 · Answer 11 · 2020-08-11 16:53:06

196

Views

Diophantine Equation with Square Root

Published on 11 Aug 2020 - 16:53

score 39 · Answer 12 · 2020-08-15 19:18:15

39

Views

Question Concerning Solutions of a Congruence that is Unique Modulo m

Published on 15 Aug 2020 - 19:18

score 266 · Answer 13 · 2020-08-15 20:19:45

266

Views

Question On Solutions for a Specific Congruence $ax \equiv 1 \pmod p$ when $p$ is prime and $p \not\mid a$

Published on 15 Aug 2020 - 20:19

score 61 · Answer 14 · 2026-03-25 08:13:37

61

Views

Qutoient monoid of kernel pair of monoid homomorphism between multiplicative naturals to additive naturals (sum of prime numbers).

Published on 25 Mar 2026 - 8:13

score 116 · Answer 15 · 2020-09-05 00:56:15

116

Views

Let R and S be binary relations on a set A. Solve for each case: If R and S are i) reflexive, ii) symmetric, iii) transitive, what would R∪S be?

Published on 05 Sep 2020 - 0:56

List Question

Show the set of congruence classes mod n is a partition of $\mathbb{Z}$.

Proof verification: Show that the set of congruence classes form a partition of $\mathbb{Z}$.

Lattices are congruence-distributive

$M_3$ is a simple lattice

CEP for Abelian groups and lattices

Quotienting a group by an equivalence relation

Every group and ring is congruence-permutable , but not necessarily congruence-distributive

For a group $G$ and subgroup $H$, is $a \sim b \iff a^{-1}b\in H$ an equivalence relation even when $H$ is not normal?

To prove that an operation is well-defined in modular arithmetic

$(\forall n \in \mathbb{Z}):n^{3} \equiv n$ (mod $6$)

Diophantine Equation with Square Root

Question Concerning Solutions of a Congruence that is Unique Modulo m

Question On Solutions for a Specific Congruence $ax \equiv 1 \pmod p$ when $p$ is prime and $p \not\mid a$

Qutoient monoid of kernel pair of monoid homomorphism between multiplicative naturals to additive naturals (sum of prime numbers).

Let R and S be binary relations on a set A. Solve for each case: If R and S are i) reflexive, ii) symmetric, iii) transitive, what would R∪S be?

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