Question

How to systematically find all the elements (ℤ/19ℤ)∗ with order 6?

score 1.9k · Answer 1 · 2026-04-15 09:58:47

1.9k

Views

How to systematically find all the elements (ℤ/19ℤ)∗ with order 6?

Published on 15 Apr 2026 - 9:58

score 926 · Answer 2 · 2026-04-17 08:15:00

926

Views

Show that $A = a^{pq} - a^{p} - a^{q} + a$ can be divided by $pq$

Published on 17 Apr 2026 - 8:15

score 100 · Answer 3 · 2026-04-11 06:31:20

100

Views

Are $\mathbb{Z}^_{28}$, $\mathbb{Z}^_{4}×\mathbb{Z}^_{7}$, $\mathbb{Z}^_{2}×\mathbb{Z}^*_{14}$ cyclic groups?

Published on 11 Apr 2026 - 6:31

score 141 · Answer 4 · 2026-04-16 10:55:25

141

Views

Prove that lcm$(a,b)$ = $k$·lcm$(a/k,b/k)$

Published on 16 Apr 2026 - 10:55

score 430 · Answer 5 · 2026-04-15 13:31:23

430

Views

$pq-6$, $qr-6$ and $rp-6$ are all perfect squares. Prove that $p+q+r-9$ is also a perfect square.

Published on 15 Apr 2026 - 13:31

score 243 · Answer 6 · 2026-04-17 11:24:00

Where does this identity come from: $\left(x^2+7xy-9y^2\right)^3+\left(2x^2-5xy+12y^2\right)^3=\left(2x^2+10y^2\right)^3+\left(x^2-9xy-y^2\right)^3$

score 60 · Answer 7 · 2026-04-16 08:22:37

60

Views

$a|b^2$ , $b^2|a^3$ , $a^3|b^4$ , $b^4| a^5$... then...

Published on 16 Apr 2026 - 8:22

score 86 · Answer 8 · 2026-04-15 07:39:53

86

Views

Find the solutions of equations of the form $ax^2+by^2 = z^2$ in $\mathbb{Q}_p$

Published on 15 Apr 2026 - 7:39

score 434 · Answer 9 · 2026-05-10 22:07:40

434

Views

Elementary question about a fake-proof and greatest common divisors

Published on 10 May 2026 - 22:07

score 177 · Answer 10 · 2026-05-10 14:32:15

177

Views

If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

Published on 10 May 2026 - 14:32

score 1.1k · Answer 11 · 2026-04-16 18:00:01

1.1k

Views

Let $p$ be an odd prime and $q$ be a prime such that $q \mid 2^p-1$ Prove that $p \mid \frac{q-1}2$

Published on 16 Apr 2026 - 18:00

score 598 · Answer 12 · 2026-04-18 03:23:24

598

Views

There are infinitely many primes $p \equiv 7 (\text{mod} \ 8).$

Published on 18 Apr 2026 - 3:23

score 235 · Answer 13 · 2026-05-10 15:03:29

235

Views

Let $p,q$ be odd primes such that $p-q=4a.$ Prove that $\Bigg(\dfrac{a}{p}\Bigg)=\Bigg(\dfrac{a}{q}\Bigg).$

Published on 10 May 2026 - 15:03

score 546 · Answer 14 · 2026-04-12 02:40:51

546

Views

A conjecture on consecutive odd composite numbers

Published on 12 Apr 2026 - 2:40

score 241 · Answer 15 · 2026-04-19 10:53:38

241

Views

$p$ and $6p+1$ both palindrome - primes. Is $(131/787)$ the only example?

Published on 19 Apr 2026 - 10:53

List Question

How to systematically find all the elements (ℤ/19ℤ)∗ with order 6?

Show that $A = a^{pq} - a^{p} - a^{q} + a$ can be divided by $pq$

Are $\mathbb{Z}^_{28}$, $\mathbb{Z}^_{4}×\mathbb{Z}^_{7}$, $\mathbb{Z}^_{2}×\mathbb{Z}^*_{14}$ cyclic groups?

Prove that lcm$(a,b)$ = $k$·lcm$(a/k,b/k)$

$pq-6$, $qr-6$ and $rp-6$ are all perfect squares. Prove that $p+q+r-9$ is also a perfect square.

Where does this identity come from: $\left(x^2+7xy-9y^2\right)^3+\left(2x^2-5xy+12y^2\right)^3=\left(2x^2+10y^2\right)^3+\left(x^2-9xy-y^2\right)^3$

$a|b^2$ , $b^2|a^3$ , $a^3|b^4$ , $b^4| a^5$... then...

Find the solutions of equations of the form $ax^2+by^2 = z^2$ in $\mathbb{Q}_p$

Elementary question about a fake-proof and greatest common divisors

If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

Let $p$ be an odd prime and $q$ be a prime such that $q \mid 2^p-1$ Prove that $p \mid \frac{q-1}2$

There are infinitely many primes $p \equiv 7 (\text{mod} \ 8).$

Let $p,q$ be odd primes such that $p-q=4a.$ Prove that $\Bigg(\dfrac{a}{p}\Bigg)=\Bigg(\dfrac{a}{q}\Bigg).$

A conjecture on consecutive odd composite numbers

$p$ and $6p+1$ both palindrome - primes. Is $(131/787)$ the only example?

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