Question

Let $x,y>1$ be coprime integers and $g>0$ a real number such that $g^x,g^y$ are both integers. Is it true that $g\in\mathbb N$?

score 123 · Answer 1 · 2026-03-26 19:02:53

123

Views

Let $x,y>1$ be coprime integers and $g>0$ a real number such that $g^x,g^y$ are both integers. Is it true that $g\in\mathbb N$?

Published on 26 Mar 2026 - 19:02

score 32 · Answer 2 · 2020-06-02 01:09:13

32

Views

Count of "minimal" divisors of $n$ greater than $Q$

Published on 02 Jun 2020 - 1:09

score 60 · Answer 3 · 2020-06-02 22:21:37

60

Views

How to compute generators in biquadratic extension

Published on 02 Jun 2020 - 22:21

score 37 · Answer 4 · 2026-03-29 02:45:38

37

Views

Prime inert in each subfields never occurs

Published on 29 Mar 2026 - 2:45

score 198 · Answer 5 · 2026-03-25 11:10:20

198

Views

Infinite primes history

Published on 25 Mar 2026 - 11:10

score 259 · Answer 6 · 2026-03-28 21:51:33

259

Views

Splitting of primes and other properties of $\mathbb{Q}[\omega]$ for $\omega=e^{2\pi i/m}$

Published on 28 Mar 2026 - 21:51

score 144 · Answer 7 · 2026-02-23 10:16:54

144

Views

Are two distinct prime factorizations relatively prime to each other?

Published on 23 Feb 2026 - 10:16

score 88 · Answer 8 · 2026-03-26 14:22:57

88

Views

Odd prime divisor of $ 3x^2+y^2$ (where $x$, $y$ are relatively prime) is again of the same form

Published on 26 Mar 2026 - 14:22

score 201 · Answer 9 · 2020-06-07 18:43:12

201

Views

$p^2+1=q^2+r^2$. Strange phenomenon of primes

Published on 07 Jun 2020 - 18:43

score 256 · Answer 10 · 2020-06-09 00:13:01

256

Views

Using the remainder theorem to prove a quadratic is a factor of a polynomial

Published on 09 Jun 2020 - 0:13

score 801 · Answer 11 · 2026-03-26 02:45:41

801

Views

Does a prime ideal contains an irreducible element?

Published on 26 Mar 2026 - 2:45

score 557 · Answer 12 · 2020-06-11 08:17:09

557

Views

Total number of times a number can be halved such that it remains a whole number

Published on 11 Jun 2020 - 8:17

score 50 · Answer 13 · 2020-06-13 17:33:56

50

Views

Prove that for $n\in\Bbb{Z}^+$, $n$ has an odd number of positive divisors if and only if $n$ is the square of an integer.

Published on 13 Jun 2020 - 17:33

score 337 · Answer 14 · 2020-06-13 18:35:38

337

Views

Prove that if $x^n + a_{n-1}x^{n-1}+ \dots + a_0 = 0$ for some integers $a_{n-1}, \dots, a_0$, then $x$ is irrational unless $x$ is an integer.

Published on 13 Jun 2020 - 18:35

score 50 · Answer 15 · 2020-06-14 16:44:07

50

Views

Are there names for the smallest Gaussian prime $1+i$ (or even $1-i$)?

Published on 14 Jun 2020 - 16:44

List Question

Let $x,y>1$ be coprime integers and $g>0$ a real number such that $g^x,g^y$ are both integers. Is it true that $g\in\mathbb N$?

Count of "minimal" divisors of $n$ greater than $Q$

How to compute generators in biquadratic extension

Prime inert in each subfields never occurs

Infinite primes history

Splitting of primes and other properties of $\mathbb{Q}[\omega]$ for $\omega=e^{2\pi i/m}$

Are two distinct prime factorizations relatively prime to each other?

Odd prime divisor of $ 3x^2+y^2$ (where $x$, $y$ are relatively prime) is again of the same form

$p^2+1=q^2+r^2$. Strange phenomenon of primes

Using the remainder theorem to prove a quadratic is a factor of a polynomial

Does a prime ideal contains an irreducible element?

Total number of times a number can be halved such that it remains a whole number

Prove that for $n\in\Bbb{Z}^+$, $n$ has an odd number of positive divisors if and only if $n$ is the square of an integer.

Prove that if $x^n + a_{n-1}x^{n-1}+ \dots + a_0 = 0$ for some integers $a_{n-1}, \dots, a_0$, then $x$ is irrational unless $x$ is an integer.

Are there names for the smallest Gaussian prime $1+i$ (or even $1-i$)?

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