Question

Let $q$, $p$ be distinct primes. Determine unique $n$ in $\{q, q+1, \ldots, q+p-1\}$ such that $\gcd(p, n) > 1$

score 51 · Answer 1 · 2016-07-31 19:16:20

51

Views

Let $q$, $p$ be distinct primes. Determine unique $n$ in $\{q, q+1, \ldots, q+p-1\}$ such that $\gcd(p, n) > 1$

Published on 31 Jul 2016 - 19:16

score 38 · Answer 2 · 2016-08-06 03:01:16

38

Views

Let $k, p, q$ be distinct primes. How to determine unique $n \in \{q, q + k, q + 2k, \ldots, q + (p - 1)k\}$ such that $\gcd(n, p) \gt 1$

Published on 06 Aug 2016 - 3:01

score 138 · Answer 3 · 2016-08-20 09:56:07

138

Views

Invariance of residues modulo $p$

Published on 20 Aug 2016 - 9:56

score 144 · Answer 4 · 2016-08-25 09:40:23

144

Views

Permutations of $\{1,\ldots,2pq\}$ modulo $2pq$

Published on 25 Aug 2016 - 9:40

score 2.2k · Answer 5 · 2016-10-06 17:28:04

2.2k

Views

What is meant by residue system and residue class in modular arithmetic?

Published on 06 Oct 2016 - 17:28

score 1.7k · Answer 6 · 2016-10-09 20:02:02

1.7k

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Show that the $k^\text{th}$ powers of a reduced residue system form a reduced residue system if and only if $(k, \phi(m)) = 1$.

Published on 09 Oct 2016 - 20:02

score 1.6k · Answer 7 · 2017-02-22 02:26:08

1.6k

Views

finding the least nonnegative residue

Published on 22 Feb 2017 - 2:26

score 2k · Answer 8 · 2017-03-06 03:33:07

2k

Views

Wilson Theorem to find least nonnegative residue modulo m

Published on 06 Mar 2017 - 3:33

score 75 · Answer 9 · 2023-02-10 15:10:49

75

Views

Existence proof of Euler's theorem

Published on 10 Feb 2023 - 15:10

score 57 · Answer 10 · 2023-11-22 13:42:46

Find all the natural numbers N such that the reduced residue system consisting of least positive residues modulo N form an arithmetic progression.

score 48 · Answer 11 · 2024-02-20 18:18:59

48

Views

Prove that $Enc_{e}(\overline{a}) = \overline{a^e}$ is a one-to-one mapping

Published on 20 Feb 2024 - 18:18

score 28 · Answer 12 · 2024-03-22 05:43:27

28

Views

prove product of a reduced residue system is congruent to 1 mod $p^{\alpha}$

Published on 22 Mar 2024 - 5:43

score 109 · Answer 13 · 2015-02-07 00:55:29

109

Views

Reasoning about the number of elements in a reduced residue system relative a primorial

Published on 07 Feb 2015 - 0:55

score 285 · Answer 14 · 2015-03-09 05:49:09

285

Views

Question about the elements of a reduced residue system relative a primorial $p_n\#$

Published on 09 Mar 2015 - 5:49

score 87 · Answer 15 · 2015-04-26 06:55:20

87

Views

Question about the Chinese Remainder Theorem and the residue class ring ${\bf Z}/p\# {\bf Z}$

Published on 26 Apr 2015 - 6:55

List Question

Let $q$, $p$ be distinct primes. Determine unique $n$ in $\{q, q+1, \ldots, q+p-1\}$ such that $\gcd(p, n) > 1$

Let $k, p, q$ be distinct primes. How to determine unique $n \in \{q, q + k, q + 2k, \ldots, q + (p - 1)k\}$ such that $\gcd(n, p) \gt 1$

Invariance of residues modulo $p$

Permutations of $\{1,\ldots,2pq\}$ modulo $2pq$

What is meant by residue system and residue class in modular arithmetic?

Show that the $k^\text{th}$ powers of a reduced residue system form a reduced residue system if and only if $(k, \phi(m)) = 1$.

finding the least nonnegative residue

Wilson Theorem to find least nonnegative residue modulo m

Existence proof of Euler's theorem

Find all the natural numbers N such that the reduced residue system consisting of least positive residues modulo N form an arithmetic progression.

Prove that $Enc_{e}(\overline{a}) = \overline{a^e}$ is a one-to-one mapping

prove product of a reduced residue system is congruent to 1 mod $p^{\alpha}$

Reasoning about the number of elements in a reduced residue system relative a primorial

Question about the elements of a reduced residue system relative a primorial $p_n\#$

Question about the Chinese Remainder Theorem and the residue class ring ${\bf Z}/p\# {\bf Z}$

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