Question

Solutions to $\left\{x^n\right\}=\{x\}^n$

score 116 · Answer 1 · 2026-03-25 21:47:59

116

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Solutions to $\left\{x^n\right\}=\{x\}^n$

Published on 25 Mar 2026 - 21:47

score 87 · Answer 2 · 2024-02-06 12:08:00

87

Views

$1^n+2^n+...+(p-1)^n$ is divisible by $p$ for $p> n+1$

Published on 06 Feb 2024 - 12:08

score 80 · Answer 3 · 2024-02-07 10:35:16

80

Views

Does the inequality $|a-b|^p \geqslant 2^{-p}|a|^p - |b|^p$ hold for every $a,b \in \mathbb R$ and $1 \leqslant p < \infty$?

Published on 07 Feb 2024 - 10:35

score 39 · Answer 4 · 2024-02-08 03:20:11

39

Views

What is the best way to find the trailing zeros of an exponentiation result without explicit computation?

Published on 08 Feb 2024 - 3:20

score 67 · Answer 5 · 2026-03-25 20:35:34

67

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Scale the sequence $a^n$ to converge to $a$

Published on 25 Mar 2026 - 20:35

score 33 · Answer 6 · 2024-02-13 16:04:29

33

Views

Comparison by Degree of Polynomial

Published on 13 Feb 2024 - 16:04

score 92 · Answer 7 · 2026-03-25 13:58:11

92

Views

Easy proof that $n=5$ is the only solution of $n^n \equiv n^{n^n} \pmod {10^{n-1}}$ if $n \in \mathbb{N}-\{0,1\}$ is not a multiple of $10$

Published on 25 Mar 2026 - 13:58

score 107 · Answer 8 · 2024-02-15 09:40:53

107

Views

Calculating $e^{j2\pi t}$ in two ways gives different results: $\cos(2\pi t)+j \sin(2\pi t)$ vs $1^t$

Published on 15 Feb 2024 - 9:40

score 69 · Answer 9 · 2024-02-22 05:52:55

69

Views

is $\sin^2 (x)$ the same as $\sin(\sin(x))$?

Published on 22 Feb 2024 - 5:52

score 69 · Answer 10 · 2026-02-23 12:01:10

69

Views

How is $\log _{10}(e)=\left[\log _e(10)\right]^{-1}$?

Published on 23 Feb 2026 - 12:01

score 189 · Answer 11 · 2026-03-30 05:12:25

189

Views

$\frac{\sin3x + 2}{\sin x+2} = 2023^{\sin x-\sin3x}$

Published on 30 Mar 2026 - 5:12

score 144 · Answer 12 · 2026-03-28 11:54:18

144

Views

$\mathcal S =\{ a^{x_i} + a^{x_j} + a^{x_k} \mid i,j,k \in \{1,2,3, \ldots,n \} , i+j+k=n \}$

Published on 28 Mar 2026 - 11:54

score 52 · Answer 13 · 2024-02-24 04:07:10

52

Views

How to calculate this expression (-1)^(2/10)?

Published on 24 Feb 2024 - 4:07

score 63 · Answer 14 · 2024-02-24 13:49:14

63

Views

If $\frac{a}{c}+\frac{b}{a}+\frac{c}{b}=a^3b+b^3c+c^3a+2$ and $a+b+c$ is different from zero show that $a=b=c$

Published on 24 Feb 2024 - 13:49

score 90 · Answer 15 · 2024-02-24 16:45:23

90

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Show that $a+b+c$ divides at least one of the following numbers: $a^3+b^3-2c^3, b^3+c^3-2a^3, a^3+c^ 3-2b^3$

Published on 24 Feb 2024 - 16:45

List Question

Solutions to $\left\{x^n\right\}=\{x\}^n$

$1^n+2^n+...+(p-1)^n$ is divisible by $p$ for $p> n+1$

Does the inequality $|a-b|^p \geqslant 2^{-p}|a|^p - |b|^p$ hold for every $a,b \in \mathbb R$ and $1 \leqslant p < \infty$?

What is the best way to find the trailing zeros of an exponentiation result without explicit computation?

Scale the sequence $a^n$ to converge to $a$

Comparison by Degree of Polynomial

Easy proof that $n=5$ is the only solution of $n^n \equiv n^{n^n} \pmod {10^{n-1}}$ if $n \in \mathbb{N}-\{0,1\}$ is not a multiple of $10$

Calculating $e^{j2\pi t}$ in two ways gives different results: $\cos(2\pi t)+j \sin(2\pi t)$ vs $1^t$

is $\sin^2 (x)$ the same as $\sin(\sin(x))$?

How is $\log _{10}(e)=\left[\log _e(10)\right]^{-1}$?

$\frac{\sin3x + 2}{\sin x+2} = 2023^{\sin x-\sin3x}$

$\mathcal S =\{ a^{x_i} + a^{x_j} + a^{x_k} \mid i,j,k \in \{1,2,3, \ldots,n \} , i+j+k=n \}$

How to calculate this expression (-1)^(2/10)?

If $\frac{a}{c}+\frac{b}{a}+\frac{c}{b}=a^3b+b^3c+c^3a+2$ and $a+b+c$ is different from zero show that $a=b=c$

Show that $a+b+c$ divides at least one of the following numbers: $a^3+b^3-2c^3, b^3+c^3-2a^3, a^3+c^ 3-2b^3$

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