Question

Is there $n \geq 2$ such that $1^1 + 2^2 + \dots + n^n$ is a perfect square?

score 321 · Answer 1 · 2018-06-11 10:27:26

321

Views

Is there $n \geq 2$ such that $1^1 + 2^2 + \dots + n^n$ is a perfect square?

Published on 11 Jun 2018 - 10:27

score 162 · Answer 2 · 2018-06-11 12:07:01

162

Views

Which positive integers $n$ can be expressed as $n=a^2+b^2+c^2$ , but not with positive $a,b,c\ $?

Published on 11 Jun 2018 - 12:07

score 102 · Answer 3 · 2026-03-19 23:27:19

102

Views

Do there exist shorter ways of solving for $x$ (or other smarter methods)?

Published on 19 Mar 2026 - 23:27

score 115 · Answer 4 · 2018-06-17 09:12:34

115

Views

Is $p^2+q^2+r^2=3^k$ with primes $p,q,r$ solvable for every odd positive integer $k\ge 3\ $?

Published on 17 Jun 2018 - 9:12

score 184 · Answer 5 · 2018-06-17 14:02:14

184

Views

Is there/can there be a model-theoretic proof of this theorem of arithmetic ?

Published on 17 Jun 2018 - 14:02

score 120 · Answer 6 · 2026-03-25 07:16:37

120

Views

Can I use the pigeon-hole principle to show that $a^2-2b^2=p$ has a solution?

Published on 25 Mar 2026 - 7:16

score 317 · Answer 7 · 2018-06-23 11:50:40

317

Views

Which natural numbers are the sum of three positive perfect squares?

Published on 23 Jun 2018 - 11:50

score 101 · Answer 8 · 2018-07-10 02:17:08

101

Views

For many integers $n$, the digit sum of $(4n^2+1)^2$ is $19$. Is there something special about $19$?

Published on 10 Jul 2018 - 2:17

score 58 · Answer 9 · 2026-03-25 04:35:12

58

Views

Case specific perfect square test: $\sqrt{x^2 + 8a}$

Published on 25 Mar 2026 - 4:35

score 264 · Answer 10 · 2018-07-24 08:29:32

264

Views

Is $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ a square number for integer $x>1$

Published on 24 Jul 2018 - 8:29

score 120 · Answer 11 · 2018-07-25 15:42:41

120

Views

When is $m^2k^2(c^2+1)^2-4mc(c^2-c+1)$ a perfect square?

Published on 25 Jul 2018 - 15:42

score 7.8k · Answer 12 · 2018-07-26 18:11:03

7.8k

Views

Is there a perfect square that is the sum of $3$ perfect squares?

Published on 26 Jul 2018 - 18:11

score 1.8k · Answer 13 · 2018-07-27 09:05:35

1.8k

Views

Summation of factorials is a perfect square number

Published on 27 Jul 2018 - 9:05

score 46 · Answer 14 · 2018-07-29 07:26:51

46

Views

Cubes and squares

Published on 29 Jul 2018 - 7:26

score 1.2k · Answer 15 · 2018-07-29 14:06:54

1.2k

Views

can anyone help me to find the square root of non perfect squares?

Published on 29 Jul 2018 - 14:06

List Question

Is there $n \geq 2$ such that $1^1 + 2^2 + \dots + n^n$ is a perfect square?

Which positive integers $n$ can be expressed as $n=a^2+b^2+c^2$ , but not with positive $a,b,c\ $?

Do there exist shorter ways of solving for $x$ (or other smarter methods)?

Is $p^2+q^2+r^2=3^k$ with primes $p,q,r$ solvable for every odd positive integer $k\ge 3\ $?

Is there/can there be a model-theoretic proof of this theorem of arithmetic ?

Can I use the pigeon-hole principle to show that $a^2-2b^2=p$ has a solution?

Which natural numbers are the sum of three positive perfect squares?

For many integers $n$, the digit sum of $(4n^2+1)^2$ is $19$. Is there something special about $19$?

Case specific perfect square test: $\sqrt{x^2 + 8a}$

Is $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ a square number for integer $x>1$

When is $m^2k^2(c^2+1)^2-4mc(c^2-c+1)$ a perfect square?

Is there a perfect square that is the sum of $3$ perfect squares?

Summation of factorials is a perfect square number

Cubes and squares

can anyone help me to find the square root of non perfect squares?

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