Question

Find $x, y\in\mathbb Z$ such that $\frac{x}{2} + \frac{x}{y} - \frac{3}{2} = \frac{10}{y}$

score 62 · Answer 1 · 2026-04-16 12:04:14

62

Views

Find $x, y\in\mathbb Z$ such that $\frac{x}{2} + \frac{x}{y} - \frac{3}{2} = \frac{10}{y}$

Published on 16 Apr 2026 - 12:04

score 84 · Answer 2 · 2026-04-12 22:54:36

84

Views

Show that $30$ divides $n^{5} - n$, where n is an integer

Published on 12 Apr 2026 - 22:54

score 194 · Answer 3 · 2026-04-09 03:58:19

194

Views

Use quadratic reciprocity to decide whether the following congruences are solvable

Published on 09 Apr 2026 - 3:58

score 262 · Answer 4 · 2026-04-17 01:05:40

Let $p$ be a prime and $a,b,c$ be integers. Prove that if $ab, ac, bc, abc$ are all quadratic residues $\mod {p}$ then so are $a, b$ and $c$.

score 44 · Answer 5 · 2026-04-17 03:48:26

Evaluate $\sum_x\big(\frac{x}{p}\big), \sum_x\big(\frac{x+k}{p}\big), \sum_x\big(\frac{ax+b}{p}\big)$ where $p$ is prime and the rests are integers.

score 190 · Answer 6 · 2026-04-16 02:46:41

190

Views

Prove that the only integer solution of the equation $a^2 + b^2 + c^2 = a^2 b^2$ is $a = b = c = 0$.

Published on 16 Apr 2026 - 2:46

score 146 · Answer 7 · 2026-04-15 22:25:21

146

Views

Find all positive integer $a,b$, such that $[a,b+2017]=[a+2017,b]$.

Published on 15 Apr 2026 - 22:25

score 468 · Answer 8 · 2026-04-14 01:18:52

468

Views

Initial values of Inkeri's primality test for Fermat numbers

Published on 14 Apr 2026 - 1:18

score 311 · Answer 9 · 2026-04-21 20:55:00

311

Views

Möbius Inversion for any Arithmetic Function

Published on 21 Apr 2026 - 20:55

score 43 · Answer 10 · 2026-04-10 10:45:22

43

Views

Modular Arithmetic Problem (Dividing by 3)

Published on 10 Apr 2026 - 10:45

score 538 · Answer 11 · 2026-04-16 11:46:09

538

Views

If $\beta$ is the transposition $\beta = (1, 4)$, compute both $\beta\alpha$ and $\beta\alpha\beta^{−1}$ and compute orders.

Published on 16 Apr 2026 - 11:46

score 59 · Answer 12 · 2026-04-15 10:13:54

59

Views

Prove if $\gcd(a,n) = g$ there are exactly $g$ solutions between $0$ and $n$ to $ax \equiv b \pmod{n}$ if $\gcd(a, n)\mid b$

Published on 15 Apr 2026 - 10:13

score 578 · Answer 13 · 2026-04-17 08:17:03

578

Views

Show that the only solutions to the congruence $x^2 \equiv 1\pmod {p^n}$ are $x \equiv \pm 1 \pmod {p^n}$

Published on 17 Apr 2026 - 8:17

score 154 · Answer 14 · 2026-04-12 02:48:54

154

Views

All pythagorean triples appear on the rational unit circle.

Published on 12 Apr 2026 - 2:48

score 40 · Answer 15 · 2026-03-25 09:29:12

40

Views

Chinese Remainder Thoerem - Is it possible to solve a system of congruences that are not coprime?

Published on 25 Mar 2026 - 9:29

List Question

Find $x, y\in\mathbb Z$ such that $\frac{x}{2} + \frac{x}{y} - \frac{3}{2} = \frac{10}{y}$

Show that $30$ divides $n^{5} - n$, where n is an integer

Use quadratic reciprocity to decide whether the following congruences are solvable

Let $p$ be a prime and $a,b,c$ be integers. Prove that if $ab, ac, bc, abc$ are all quadratic residues $\mod {p}$ then so are $a, b$ and $c$.

Evaluate $\sum_x\big(\frac{x}{p}\big), \sum_x\big(\frac{x+k}{p}\big), \sum_x\big(\frac{ax+b}{p}\big)$ where $p$ is prime and the rests are integers.

Prove that the only integer solution of the equation $a^2 + b^2 + c^2 = a^2 b^2$ is $a = b = c = 0$.

Find all positive integer $a,b$, such that $[a,b+2017]=[a+2017,b]$.

Initial values of Inkeri's primality test for Fermat numbers

Möbius Inversion for any Arithmetic Function

Modular Arithmetic Problem (Dividing by 3)

If $\beta$ is the transposition $\beta = (1, 4)$, compute both $\beta\alpha$ and $\beta\alpha\beta^{−1}$ and compute orders.

Prove if $\gcd(a,n) = g$ there are exactly $g$ solutions between $0$ and $n$ to $ax \equiv b \pmod{n}$ if $\gcd(a, n)\mid b$

Show that the only solutions to the congruence $x^2 \equiv 1\pmod {p^n}$ are $x \equiv \pm 1 \pmod {p^n}$

All pythagorean triples appear on the rational unit circle.

Chinese Remainder Thoerem - Is it possible to solve a system of congruences that are not coprime?

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