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kantatu pro download gratis em portuguesQ:

$np$ is the order of $n$ in $\mathbb Z_n$. Why is it true?

I understand that $\phi(n)$ divides $n$, and that $\phi(p)=p-1$. But why does $p \mid n$, and $n = 1 \cdot p + 1 \cdot p^2 + 1 \cdot p^3 +… $ imply that $n \mid np$?

A:

Let $n=p^am$ where $a\ge 1$. Then $n\mid np$.

A:

$$n=\underbrace{1\cdot p+1\cdot p^2+1\cdot p^3+\cdots+1\cdot p^m}_m$$
$$=\underbrace{1\cdot p}_{=p-1}\cdot m+\underbrace{1\cdot p^2}_{=p}\cdot m+\underbrace{1\cdot p^3}_{=p^2-1}\cdot m+\cdots+\underbrace{1\cdot p^m}_{=p^{m-1}-1}\cdot m$$
$$\implies np=\underbrace{1\cdot p}_{=p-1}\cdot m^2+\underbrace{1\cdot p^2}_{=p}\cdot m^2+\underbrace{1\cdot p^3}_{=p^2-1}\cdot m^2+\cdots+\underbrace{1\cdot p^{m-1}}_{=p^{m-2}-1}\cdot m^2$$

A:

When we say that $\phi(n)$ divides $n$ we mean that $\varphi(n) = \prod_{i=1}^{\infty} p_i^{k_i}$ where $p_i$ is the $i$th prime and $\prod_{i=1}^{\infty} p_i^{k_i} = \varphi(n)$.
We know that $

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We do not host or upload any video, films, or media files on this server. The answers provided on this site should not be used for diagnosing or treating a health problem or a disease. It is not intended to be a substitute for professional advice. If you have or suspect you may have a health problem, you should consult your healthcare provider.The present invention relates to a system and method for performing a slow and rapid diagnostic and/or treatment procedures on a subject. More specifically, the present invention relates to a device for providing both cardiac diagnostic and/or treatment procedures and neurological diagnostic and/or treatment procedures at substantially the same time.
The cardiac field is currently using catheter-based medical procedures for a variety of treatments. These treatments include the use of balloon or basket catheters, stent delivery catheters, electrophysiology (EP) catheters, etc. In a common method of treatment, a catheter is inserted into a patient””s vasculature and guided to the site where a medical procedure is to be performed. The catheter may be guided by a hollow needle, known as a trocar, or a catheter may simply be inserted into a blood vessel. The trocar is then removed, leaving the catheter in place. The catheter may then be equipped with one or more medical devices, which are used to complete the medical procedure. For example, the catheter may be used to deliver treatment agents, such as therapeutic agents, drugs, etc., to a preselected location, in the subject. The catheter may also be used to deliver diagnostic agents to a preselected
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