Question

Show that the cube of any integer is congruent to $0$ or $\pm 1 \pmod 7 $

score 4.9k · Answer 1 · 2016-05-17 16:08:43

4.9k

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Show that the cube of any integer is congruent to $0$ or $\pm 1 \pmod 7 $

Published on 17 May 2016 - 16:08

score 355 · Answer 2 · 2026-03-25 23:37:15

355

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Why the upper bound on parameters of a Linear Congruential Generator?

Published on 25 Mar 2026 - 23:37

score 136 · Answer 3 · 2026-03-30 17:34:59

136

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Elementary Number Theory: Chinese Remainder Theorem

Published on 30 Mar 2026 - 17:34

score 43 · Answer 4 · 2016-05-21 13:26:09

43

Views

$p \in \Bbb P, a \in \Bbb N$, then if $ord_p(a)=d$ we have $a^{d-1}+\dots+a+1 \equiv 0 \mod p$.

Published on 21 May 2016 - 13:26

score 79 · Answer 5 · 2016-05-21 22:48:58

79

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Proving primality of $p$ without making any calculation involving $p$ directly

Published on 21 May 2016 - 22:48

score 45 · Answer 6 · 2016-05-24 01:22:57

45

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Solutions in $\mathbb Q_p$ leads to solution for congruences equations?

Published on 24 May 2016 - 1:22

score 40 · Answer 7 · 2016-05-25 16:32:24

40

Views

Find the remainder for $\sum_{i=1}^{n} (-1)^i \cdot i!$ when dividing by 36 $\forall n \in \Bbb N$

Published on 25 May 2016 - 16:32

score 150 · Answer 8 · 2016-05-25 18:43:17

150

Views

Prove that if $p \mid a-b$ then $p^{n+1} \mid a^{p^n}-b^{p^n}$

Published on 25 May 2016 - 18:43

score 4.4k · Answer 9 · 2016-05-26 16:46:44

4.4k

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Proving that an equation doesn't have integer solutions

Published on 26 May 2016 - 16:46

score 1.2k · Answer 10 · 2016-05-29 05:57:10

1.2k

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Find a solution to the congruence $x^3 \equiv$ $4 $ mod $ 5$

Published on 29 May 2016 - 5:57

score 1k · Answer 11 · 2026-03-28 22:55:25

1k

Views

How do you solve $x^2 - 4 \equiv 0 \mod 21$

Published on 28 Mar 2026 - 22:55

score 401 · Answer 12 · 2026-03-27 04:24:18

401

Views

Congruence for Bernoulli numbers

Published on 27 Mar 2026 - 4:24

score 61 · Answer 13 · 2016-05-30 04:06:35

61

Views

Find $b \in \Bbb Z$ for which exists $a \equiv 4 \pmod 5$ such that $6a+21b=15$

Published on 30 May 2016 - 4:06

score 264 · Answer 14 · 2016-05-30 05:05:29

264

Views

How do I show that the product of even and odd number is always congruent to 2 modulo 4?

Published on 30 May 2016 - 5:05

score 73 · Answer 15 · 2016-05-30 07:38:25

73

Views

Simultaneous congruence relations $x^a \equiv 1\pmod p$ and $x^b \equiv 1\pmod p$

Published on 30 May 2016 - 7:38

List Question

Show that the cube of any integer is congruent to $0$ or $\pm 1 \pmod 7 $

Why the upper bound on parameters of a Linear Congruential Generator?

Elementary Number Theory: Chinese Remainder Theorem

$p \in \Bbb P, a \in \Bbb N$, then if $ord_p(a)=d$ we have $a^{d-1}+\dots+a+1 \equiv 0 \mod p$.

Proving primality of $p$ without making any calculation involving $p$ directly

Solutions in $\mathbb Q_p$ leads to solution for congruences equations?

Find the remainder for $\sum_{i=1}^{n} (-1)^i \cdot i!$ when dividing by 36 $\forall n \in \Bbb N$

Prove that if $p \mid a-b$ then $p^{n+1} \mid a^{p^n}-b^{p^n}$

Proving that an equation doesn't have integer solutions

Find a solution to the congruence $x^3 \equiv$ $4 $ mod $ 5$

How do you solve $x^2 - 4 \equiv 0 \mod 21$

Congruence for Bernoulli numbers

Find $b \in \Bbb Z$ for which exists $a \equiv 4 \pmod 5$ such that $6a+21b=15$

How do I show that the product of even and odd number is always congruent to 2 modulo 4?

Simultaneous congruence relations $x^a \equiv 1\pmod p$ and $x^b \equiv 1\pmod p$

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