Question

A finite set $S$ containing no perfect powers such that, for any prime $p$, $x^n\equiv s\pmod{p}$ has a solution $(x,s)\in\mathbb{Z}\times S$

score 175 · Answer 1 · 2026-04-15 18:45:20

175

Views

A finite set $S$ containing no perfect powers such that, for any prime $p$, $x^n\equiv s\pmod{p}$ has a solution $(x,s)\in\mathbb{Z}\times S$

Published on 15 Apr 2026 - 18:45

score 206 · Answer 2 · 2026-04-13 20:22:31

206

Views

What is the smallest size of a set $S$ with some extra conditions such that $S$ contains an $n$-th power residue for each prime $p$?

Published on 13 Apr 2026 - 20:22

score 49 · Answer 3 · 2026-04-15 23:05:01

49

Views

How many modular inverse number pairs between $0$ and $n$?

Published on 15 Apr 2026 - 23:05

score 74 · Answer 4 · 2026-03-25 16:02:38

74

Views

Finding solutions to $x^2\equiv a$ mod $8k+1$, $8k+1$ prime

Published on 25 Mar 2026 - 16:02

score 98 · Answer 5 · 2026-04-14 14:42:46

98

Views

Finding all $z$ which satisfy $|\Re(z^2)| \equiv |\Re(z)|$ and $|\Im(z^2)| \equiv |\Im(z)|$

Published on 14 Apr 2026 - 14:42

score 371 · Answer 6 · 2026-04-11 11:14:33

371

Views

If an infinite set $S$ of positive integers is equidistributed, is $S+S$ also equidistributed?

Published on 11 Apr 2026 - 11:14

score 683 · Answer 7 · 2026-04-16 04:59:02

683

Views

Let $p$ be a prime number for which also $p^2+2$ is a prime. Show that then $p^3+2$ is also a prime.

Published on 16 Apr 2026 - 4:59

score 622 · Answer 8 · 2026-04-10 18:02:27

622

Views

Solvability condition for congruences systems

Published on 10 Apr 2026 - 18:02

score 53 · Answer 9 · 2026-04-14 01:33:45

53

Views

What can be an expression for $n \mod (a+b)$?

Published on 14 Apr 2026 - 1:33

score 82 · Answer 10 · 2026-03-28 12:02:56

82

Views

Proving two distinct primitive roots do not generate $\mathbb{Z}^{\times}_n$ in the same order

Published on 28 Mar 2026 - 12:02

score 68 · Answer 11 · 2026-04-09 04:05:16

68

Views

How to efficiently calculate $a^k \bmod m$

Published on 09 Apr 2026 - 4:05

score 52 · Answer 12 · 2026-03-25 12:50:03

52

Views

What is the "right" name for this Diophantine equation? $ a_1 x_1 + a_2 x_2 + \dots + a_k x_k \equiv n\pmod h$

Published on 25 Mar 2026 - 12:50

score 388 · Answer 13 · 2026-04-15 03:50:29

388

Views

When Is $a^{\phi(n)+1}\equiv a \pmod n$ true?

Published on 15 Apr 2026 - 3:50

score 39 · Answer 14 · 2026-04-16 12:04:53

39

Views

Is $\binom{N}{b}\equiv a\mod N,$ $a\neq 0$, only possibly when $\gcd(N,b)>1$?

Published on 16 Apr 2026 - 12:04

score 188 · Answer 15 · 2026-04-15 06:17:30

188

Views

Polynomial zeros modulo a prime power

Published on 15 Apr 2026 - 6:17

List Question

A finite set $S$ containing no perfect powers such that, for any prime $p$, $x^n\equiv s\pmod{p}$ has a solution $(x,s)\in\mathbb{Z}\times S$

What is the smallest size of a set $S$ with some extra conditions such that $S$ contains an $n$-th power residue for each prime $p$?

How many modular inverse number pairs between $0$ and $n$?

Finding solutions to $x^2\equiv a$ mod $8k+1$, $8k+1$ prime

Finding all $z$ which satisfy $|\Re(z^2)| \equiv |\Re(z)|$ and $|\Im(z^2)| \equiv |\Im(z)|$

If an infinite set $S$ of positive integers is equidistributed, is $S+S$ also equidistributed?

Let $p$ be a prime number for which also $p^2+2$ is a prime. Show that then $p^3+2$ is also a prime.

Solvability condition for congruences systems

What can be an expression for $n \mod (a+b)$?

Proving two distinct primitive roots do not generate $\mathbb{Z}^{\times}_n$ in the same order

How to efficiently calculate $a^k \bmod m$

What is the "right" name for this Diophantine equation? $ a_1 x_1 + a_2 x_2 + \dots + a_k x_k \equiv n\pmod h$

When Is $a^{\phi(n)+1}\equiv a \pmod n$ true?

Is $\binom{N}{b}\equiv a\mod N,$ $a\neq 0$, only possibly when $\gcd(N,b)>1$?

Polynomial zeros modulo a prime power

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