Question

Chinese remainder Theorem when GCD is > 1

score 75 · Answer 1 · 2021-07-16 09:16:03

75

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Chinese remainder Theorem when GCD is > 1

Published on 16 Jul 2021 - 9:16

score 583 · Answer 2 · 2021-07-18 22:15:17

583

Views

If $I$ and $J$ are Ideals of a commutative ring $R$ where $I + J = R$, then $c \equiv a \pmod I$ and $c \equiv b \pmod J$.

Published on 18 Jul 2021 - 22:15

score 84 · Answer 3 · 2021-07-21 21:50:05

84

Views

Can we use Chinese remainder theorem to "shrink" a field?

Published on 21 Jul 2021 - 21:50

score 73 · Answer 4 · 2021-07-24 19:19:56

73

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Can we use Chinese remainder theorem to "shrink" a field? attempt 2

Published on 24 Jul 2021 - 19:19

score 89 · Answer 5 · 2021-07-26 20:57:52

89

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Congruence system \begin{cases} 3x \equiv 4 \pmod{7}\\ 5x \equiv 9 \pmod{11} \end{cases}

Published on 26 Jul 2021 - 20:57

score 125 · Answer 6 · 2021-08-03 00:34:39

125

Views

Show that there are arbitrarily large intervals of consecutive integers, none of which is free of squares.

Published on 03 Aug 2021 - 0:34

score 509 · Answer 7 · 2021-08-15 12:18:43

509

Views

Tensor product $L \otimes_K L$ has no nilpotent elements iff $I/I^2=0$

Published on 15 Aug 2021 - 12:18

score 267 · Answer 8 · 2021-08-21 15:34:40

267

Views

What is the property of co-primes that allows CRT to work?

Published on 21 Aug 2021 - 15:34

score 47 · Answer 9 · 2021-08-29 14:32:52

47

Views

Finding all vectors $(x_1, x_2, x_3) \in \mathbb{Z}_{2021^2}^3$ such $x_1x_2x_3 \equiv 43 \;(\text{mod } 2021^2)$

Published on 29 Aug 2021 - 14:32

score 71 · Answer 10 · 2021-09-07 11:04:44

71

Views

Chinese Remainder Theorem - unclear step in algorithm

Published on 07 Sep 2021 - 11:04

score 723 · Answer 11 · 2021-09-12 12:39:28

723

Views

Find a solution to congruence system $x\equiv 3\pmod{7}$ and $x\equiv 9\pmod{13}$

Published on 12 Sep 2021 - 12:39

score 84 · Answer 12 · 2021-09-18 09:17:07

84

Views

How to find a number $n$ when $n$ mod $n_1$ and $n$ mod $n_2$ is given?

Published on 18 Sep 2021 - 9:17

score 90 · Answer 13 · 2021-09-26 11:12:21

90

Views

Are these incremements a valid/useful pattern when mapping between modulo (crt)

Published on 26 Sep 2021 - 11:12

score 192 · Answer 14 · 2021-10-01 15:18:27

192

Views

Small lemma on moving up multiplicative inverses of powers needs explanation

Published on 01 Oct 2021 - 15:18

score 127 · Answer 15 · 2021-10-04 03:45:26

127

Views

Prove that $x^2+3=0 \text{ can be solved in } \mathbb{Z}/7^k\mathbb{Z} \quad \forall k$.

Published on 04 Oct 2021 - 3:45

List Question

Chinese remainder Theorem when GCD is > 1

If $I$ and $J$ are Ideals of a commutative ring $R$ where $I + J = R$, then $c \equiv a \pmod I$ and $c \equiv b \pmod J$.

Can we use Chinese remainder theorem to "shrink" a field?

Can we use Chinese remainder theorem to "shrink" a field? attempt 2

Congruence system \begin{cases} 3x \equiv 4 \pmod{7}\\ 5x \equiv 9 \pmod{11} \end{cases}

Show that there are arbitrarily large intervals of consecutive integers, none of which is free of squares.

Tensor product $L \otimes_K L$ has no nilpotent elements iff $I/I^2=0$

What is the property of co-primes that allows CRT to work?

Finding all vectors $(x_1, x_2, x_3) \in \mathbb{Z}_{2021^2}^3$ such $x_1x_2x_3 \equiv 43 \;(\text{mod } 2021^2)$

Chinese Remainder Theorem - unclear step in algorithm

Find a solution to congruence system $x\equiv 3\pmod{7}$ and $x\equiv 9\pmod{13}$

How to find a number $n$ when $n$ mod $n_1$ and $n$ mod $n_2$ is given?

Are these incremements a valid/useful pattern when mapping between modulo (crt)

Small lemma on moving up multiplicative inverses of powers needs explanation

Prove that $x^2+3=0 \text{ can be solved in } \mathbb{Z}/7^k\mathbb{Z} \quad \forall k$.

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