Tagged Questions
8
votes
1answer
210 views
Is it possible to prove the positive root of the equation ${^4}x=2$, $x=1.4466014324…$ is irrational?
(somewhat related to my earlier question)
Let ${^n}a$ denote tetration $\underbrace{a^{a^{.^{.^{.^a}}}}}_{n \text{ times}}$ (or, defined recursively, ${^1}a=a$, ${^{n+1}}a=a^{({^n}a)}$).
The ...
4
votes
4answers
66 views
Can you raise a Matrix to a non integer number? [duplicate]
So I heard you can take a matrix A to the power 2, take it to a -3th power and multiply it by an irrational number. You can also do some other non-intuitive things like taking e to the power of a ...
1
vote
0answers
117 views
What is the exact definition of a rational power?
I was taught in school that
$$x^{a/b} = \sqrt[b]{x^a}$$
however, wolfram says this is not always true:
$\sqrt[3]{x^2} \ne x^{2/3}$
...
1
vote
0answers
71 views
Are limits on exponents in moduli possible, if the modulus is relatively prime?
I asked a similar question to this recently. Here, I consider an arbitrary, but fixed, modulus m, which is relatively prime to x and y. Can anybody extend the answer given in the previous question?
...
4
votes
1answer
146 views
Are limits on exponents in moduli possible?
Suppose I show that:
$$x^{f(z)/g(z)} = y \pmod{4}$$
is impossible for some given positive integers $x$ and $y$, where,
\begin{align*}
f(z) &= \phi(4) k_1(z) + 1 \\
&= 2 k_1(z) + 1\\
g(z) ...
