Question

Do there exist any positive integers $n$ such that $\lfloor{e^n}\rfloor$ is a perfect power? What is the probability that one exists?

score 147 · Answer 1 · 2026-03-17 05:05:55

147

Views

Do there exist any positive integers $n$ such that $\lfloor{e^n}\rfloor$ is a perfect power? What is the probability that one exists?

Published on 17 Mar 2026 - 5:05

score 191 · Answer 2 · 2026-03-23 04:44:35

191

Views

Solving $x^2+x+1=7^n$

Published on 23 Mar 2026 - 4:44

score 78 · Answer 3 · 2026-03-22 21:04:00

78

Views

Are there more non-trivial powers of the form $S_p$?

Published on 22 Mar 2026 - 21:04

score 139 · Answer 4 · 2026-03-17 15:01:56

139

Views

What is the largest number whose first digits can be calculated?

Published on 17 Mar 2026 - 15:01

score 176 · Answer 5 · 2026-03-17 03:42:39

176

Views

Density of n-th Power of Rationals in $\mathbb{Q}$

Published on 17 Mar 2026 - 3:42

score 154 · Answer 6 · 2026-03-17 03:05:32

154

Views

Is there another prime $p$ such that $S(p)$ is prime?

Published on 17 Mar 2026 - 3:05

score 70 · Answer 7 · 2026-03-17 11:55:39

70

Views

Which cycles are possible by repeated summation of the cubes of the digits of a number?

Published on 17 Mar 2026 - 11:55

score 95 · Answer 8 · 2026-03-22 08:46:32

95

Views

Naturals representable as differences of powers

Published on 22 Mar 2026 - 8:46

score 66 · Answer 9 · 2026-03-22 03:02:47

66

Views

Waring’s analogue for fractions?

Published on 22 Mar 2026 - 3:02

score 456 · Answer 10 · 2026-03-16 20:30:22

456

Views

Number of elements $n \in \{1, ..., 100 \}$ such that $n^{4} - 20n^{2} + 100$ is of the form $k^{4}$ with $k$ an integer.

Published on 16 Mar 2026 - 20:30

score 56 · Answer 11 · 2026-03-16 20:02:19

56

Views

Are there only finite many n-tupels of factorials summing up to a non-trivial power?

Published on 16 Mar 2026 - 20:02

score 78 · Answer 12 · 2026-03-17 16:07:23

78

Views

Which are the solutions of $a^2+b^3=c^6$ with coprime integers $a,b,c$?

Published on 17 Mar 2026 - 16:07

score 162 · Answer 13 · 2026-03-22 00:56:10

162

Views

Is this set of solutions complete?

Published on 22 Mar 2026 - 0:56

score 102 · Answer 14 · 2026-03-17 19:55:55

102

Views

"Schäffer's conjecture" on equation $1^k+2^k+\cdots+x^k=y^n$

Published on 17 Mar 2026 - 19:55

score 299 · Answer 15 · 2026-03-17 06:18:40

299

Views

For any integer n, $78n^2+72n+2018$ is expressed as sum of four perfect cubes.

Published on 17 Mar 2026 - 6:18

List Question

Do there exist any positive integers $n$ such that $\lfloor{e^n}\rfloor$ is a perfect power? What is the probability that one exists?

Solving $x^2+x+1=7^n$

Are there more non-trivial powers of the form $S_p$?

What is the largest number whose first digits can be calculated?

Density of n-th Power of Rationals in $\mathbb{Q}$

Is there another prime $p$ such that $S(p)$ is prime?

Which cycles are possible by repeated summation of the cubes of the digits of a number?

Naturals representable as differences of powers

Waring’s analogue for fractions?

Number of elements $n \in \{1, ..., 100 \}$ such that $n^{4} - 20n^{2} + 100$ is of the form $k^{4}$ with $k$ an integer.

Are there only finite many n-tupels of factorials summing up to a non-trivial power?

Which are the solutions of $a^2+b^3=c^6$ with coprime integers $a,b,c$?

Is this set of solutions complete?

"Schäffer's conjecture" on equation $1^k+2^k+\cdots+x^k=y^n$

For any integer n, $78n^2+72n+2018$ is expressed as sum of four perfect cubes.

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