Question

Can $!1+!2+!3+\cdots+!n$ be a perfect power?

score 299 · Answer 1 · 2023-09-27 08:44:24

299

Views

Can $!1+!2+!3+\cdots+!n$ be a perfect power?

Published on 27 Sep 2023 - 8:44

score 164 · Answer 2 · 2023-11-23 02:46:16

164

Views

Is $1 \times 1 + 2 \times 2 + 3 \times 4 + 4 \times 8 = 49$ a coincidence? (Is $\sum_{i=0}^k(i+1)2^i$ ever a square again?)

Published on 23 Nov 2023 - 2:46

score 46 · Answer 3 · 2023-11-24 12:14:14

46

Views

Are $8, 36, 216,$ and $2304$ the only perfect powers that is $6$ less or more than a primorial?

Published on 24 Nov 2023 - 12:14

score 617 · Answer 4 · 2023-12-06 17:46:43

617

Views

Can $1\underbrace{44\cdots4}_{n\text{ times}}$ be a perfect power in other bases?

Published on 06 Dec 2023 - 17:46

score 128 · Answer 5 · 2023-12-07 23:11:56

128

Views

The Diophantine equation $A^{15} + B^5 + C^5 + D^5 = E^{10}$

Published on 07 Dec 2023 - 23:11

score 69 · Answer 6 · 2023-12-19 12:28:22

69

Views

Faulhaber , primes and irreducible : $S_p(n)=\sum_{k=1}^nk^p = n^a (n+1)^b F_p(n)$

Published on 19 Dec 2023 - 12:28

score 161 · Answer 7 · 2026-03-25 20:35:54

161

Views

Is this 3D algebra $T$ power-associative?

Published on 25 Mar 2026 - 20:35

score 1.4k · Answer 8 · 2023-12-31 04:30:31

1.4k

Views

Does there exist a positive integer value of $n$ such that the sum of $1!^n+2!^n+3!^n+\cdots+2024!^n$ is a perfect power?

Published on 31 Dec 2023 - 4:30

score 323 · Answer 9 · 2024-01-10 11:58:05

323

Views

Except for $1$, are there any perfect powers in the sequence $1,21,321,4321,\cdots$?

Published on 10 Jan 2024 - 11:58

score 107 · Answer 10 · 2026-03-25 09:32:11

107

Views

Does $(x^2)(x^3) \neq 0$ imply $(x)(x^3) \neq 0$?

Published on 25 Mar 2026 - 9:32

score 379 · Answer 11 · 2024-01-22 03:14:19

379

Views

Proving existence of powers of 10 in a sequence

Published on 22 Jan 2024 - 3:14

score 176 · Answer 12 · 2024-01-27 10:50:02

176

Views

when could $5^m+5^n$ represented as sum of two squares

Published on 27 Jan 2024 - 10:50

score 352 · Answer 13 · 2024-02-02 00:56:41

352

Views

Can the sum of $2025$ consecutive factorials be a perfect power?

Published on 02 Feb 2024 - 0:56

score 100 · Answer 14 · 2024-02-04 20:01:55

100

Views

Consecutive numbers of the form $n^m + m^{n + 1}$

Published on 04 Feb 2024 - 20:01

score 127 · Answer 15 · 2024-02-09 03:20:25

127

Views

Is $357911$ the only perfect power that is obtained by concatenating $5$ or more consecutive odd numbers(in decimal)?

Published on 09 Feb 2024 - 3:20

List Question

Can $!1+!2+!3+\cdots+!n$ be a perfect power?

Is $1 \times 1 + 2 \times 2 + 3 \times 4 + 4 \times 8 = 49$ a coincidence? (Is $\sum_{i=0}^k(i+1)2^i$ ever a square again?)

Are $8, 36, 216,$ and $2304$ the only perfect powers that is $6$ less or more than a primorial?

Can $1\underbrace{44\cdots4}_{n\text{ times}}$ be a perfect power in other bases?

The Diophantine equation $A^{15} + B^5 + C^5 + D^5 = E^{10}$

Faulhaber , primes and irreducible : $S_p(n)=\sum_{k=1}^nk^p = n^a (n+1)^b F_p(n)$

Is this 3D algebra $T$ power-associative?

Does there exist a positive integer value of $n$ such that the sum of $1!^n+2!^n+3!^n+\cdots+2024!^n$ is a perfect power?

Except for $1$, are there any perfect powers in the sequence $1,21,321,4321,\cdots$?

Does $(x^2)(x^3) \neq 0$ imply $(x)(x^3) \neq 0$?

Proving existence of powers of 10 in a sequence

when could $5^m+5^n$ represented as sum of two squares

Can the sum of $2025$ consecutive factorials be a perfect power?

Consecutive numbers of the form $n^m + m^{n + 1}$

Is $357911$ the only perfect power that is obtained by concatenating $5$ or more consecutive odd numbers(in decimal)?

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