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 52 · Answer 1 · 2026-03-25 09:29:06

52

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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 25 Mar 2026 - 9:29

score 39 · Answer 2 · 2026-03-25 09:29:55

39

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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 25 Mar 2026 - 9:29

score 139 · Answer 3 · 2026-03-25 10:55:41

139

Views

Invariance of residues modulo $p$

Published on 25 Mar 2026 - 10:55

score 145 · Answer 4 · 2026-03-25 09:25:31

145

Views

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

Published on 25 Mar 2026 - 9:25

score 2.2k · Answer 5 · 2026-03-25 11:06:22

2.2k

Views

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

Published on 25 Mar 2026 - 11:06

score 1.7k · Answer 6 · 2026-03-25 09:29:18

1.7k

Views

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 25 Mar 2026 - 9:29

score 1.6k · Answer 7 · 2026-03-25 09:23:40

1.6k

Views

finding the least nonnegative residue

Published on 25 Mar 2026 - 9:23

score 2k · Answer 8 · 2026-03-25 10:54:14

2k

Views

Wilson Theorem to find least nonnegative residue modulo m

Published on 25 Mar 2026 - 10:54

score 76 · Answer 9 · 2026-03-25 09:23:25

76

Views

Existence proof of Euler's theorem

Published on 25 Mar 2026 - 9:23

score 58 · Answer 10 · 2026-03-25 09:30:02

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

score 49 · Answer 11 · 2026-03-25 09:25:33

49

Views

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

Published on 25 Mar 2026 - 9:25

score 31 · Answer 12 · 2026-04-16 09:59:42

31

Views

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

Published on 16 Apr 2026 - 9:59

score 110 · Answer 13 · 2026-03-25 09:28:39

110

Views

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

Published on 25 Mar 2026 - 9:28

score 286 · Answer 14 · 2026-03-25 09:27:44

286

Views

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

Published on 25 Mar 2026 - 9:27

score 88 · Answer 15 · 2026-03-25 11:06:41

88

Views

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

Published on 25 Mar 2026 - 11:06

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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