Question

Power Tower leads to a seeming contradiction

score 48 · Answer 1 · 2026-04-15 03:05:03

48

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Power Tower leads to a seeming contradiction

Published on 15 Apr 2026 - 3:05

score 51 · Answer 2 · 2026-04-17 10:00:21

51

Views

Show that $n^{n^{n^4}} - n^{n^{n^2}} \equiv 0 (\mod 547)$

Published on 17 Apr 2026 - 10:00

score 21 · Answer 3 · 2026-04-15 02:59:23

21

Views

Does $a_3 \in \mathbb{R}$ always exist s.t. $a_1 \cdot x \cdot a_2^c = x \cdot a_3^c \forall a_1, a_2, x, c \in \mathbb{R}$?

Published on 15 Apr 2026 - 2:59

score 72 · Answer 4 · 2026-04-12 09:51:17

72

Views

I have encountered a problem in solving this number theory problem

Published on 12 Apr 2026 - 9:51

score 64 · Answer 5 · 2026-04-16 07:45:41

Proving $\lim_{n(\in\mathbb{N})\rightarrow\infty}\left(1+\frac{1}{n}\right)^{nx} \equiv \sum_0^\infty\frac{x^k}{k!}$ for all rational $x$

score 160 · Answer 6 · 2026-04-15 22:59:31

160

Views

Why is √(x²) the same as |x|, instead of ±x?

Published on 15 Apr 2026 - 22:59

score 142 · Answer 7 · 2026-04-15 22:57:40

142

Views

Why is $i^i$ real but not $\left(\frac{1+i}{\sqrt{2}}\right)^i$?

Published on 15 Apr 2026 - 22:57

score 68 · Answer 8 · 2026-04-16 15:35:39

68

Views

Show that $\lim_{n \rightarrow \infty}x^{a_n} = x^{L}$ if $(a_i)_{i=1}^{\infty}$ is a sequence of real numbers that converges to $L$

Published on 16 Apr 2026 - 15:35

score 86 · Answer 9 · 2026-04-14 05:06:52

86

Views

How to use the $x^n - a^n$ factoring pattern if $n$ is not an integer?

Published on 14 Apr 2026 - 5:06

score 74 · Answer 10 · 2026-04-17 10:34:46

74

Views

Solving $x^{-x^{1-x}}=\sqrt[\sqrt2]{2}$

Published on 17 Apr 2026 - 10:34

score 114 · Answer 11 · 2026-04-16 06:08:30

114

Views

Find real and imaginary parts of real to the power of a positive real

Published on 16 Apr 2026 - 6:08

score 97 · Answer 12 · 2026-04-16 15:19:52

97

Views

When $2^{2012}$ is multiplied by $5^{2013}$, what is the sum of all the digits in the product?

Published on 16 Apr 2026 - 15:19

score 93 · Answer 13 · 2026-04-09 23:13:16

93

Views

Why did we stop creating functions at exponents?

Published on 09 Apr 2026 - 23:13

score 34 · Answer 14 · 2026-04-15 08:06:45

34

Views

Nomenclature of power functions and their graphs

Published on 15 Apr 2026 - 8:06

score 37 · Answer 15 · 2026-04-16 14:02:28

37

Views

Am I correct in calculating/getting this answer? (Exponent Laws)

Published on 16 Apr 2026 - 14:02

List Question

Power Tower leads to a seeming contradiction

Show that $n^{n^{n^4}} - n^{n^{n^2}} \equiv 0 (\mod 547)$

Does $a_3 \in \mathbb{R}$ always exist s.t. $a_1 \cdot x \cdot a_2^c = x \cdot a_3^c \forall a_1, a_2, x, c \in \mathbb{R}$?

I have encountered a problem in solving this number theory problem

Proving $\lim_{n(\in\mathbb{N})\rightarrow\infty}\left(1+\frac{1}{n}\right)^{nx} \equiv \sum_0^\infty\frac{x^k}{k!}$ for all rational $x$

Why is √(x²) the same as |x|, instead of ±x?

Why is $i^i$ real but not $\left(\frac{1+i}{\sqrt{2}}\right)^i$?

Show that $\lim_{n \rightarrow \infty}x^{a_n} = x^{L}$ if $(a_i)_{i=1}^{\infty}$ is a sequence of real numbers that converges to $L$

How to use the $x^n - a^n$ factoring pattern if $n$ is not an integer?

Solving $x^{-x^{1-x}}=\sqrt[\sqrt2]{2}$

Find real and imaginary parts of real to the power of a positive real

When $2^{2012}$ is multiplied by $5^{2013}$, what is the sum of all the digits in the product?

Why did we stop creating functions at exponents?

Nomenclature of power functions and their graphs

Am I correct in calculating/getting this answer? (Exponent Laws)

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