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安裝中文字典英文字典辭典工具!
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- Show that if $p gt; 1$ and $p|(p-1)! +1$, then $p$ is prime.
Hint $\ $ If $\,p\,$ is composite then it has a proper factor $\,d,\,$ i e $\,d\mid p\,$ and $\, 1 < d < p \,$ Then
- elementary number theory - Show the $(p-1)! \equiv -1 \mod p . . .
So,the numbers $2, \dots,p-2$ can be seperated into $\frac{p-3}{2}$ pairs,so that the product of the two numbers of each pair is equivalent $\pmod p$ to $1$,and therefore: $$2 \cdots (p-2) \equiv 1 \pmod p$$
- number theory - When is $(p - 1)! + 1$ a power of $p$? - Mathematics . . .
A friend asked me this question: If $p$ is a prime, prove that $(p - 1)! + 1$ is a power of $p$ if and only if $p = 2, 3$ or $5$
- convergence divergence - What is the product of $p_i-1 \over p_i . . .
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- Prove that $(p-1)! \\equiv (p-1) \\pmod{1+2+3+\\cdots+(p-1)}$
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- Binomial distribution p=1 - Mathematics Stack Exchange
Because you will have $0^{0}$ which is indeterminate and conveniently equal to 1 and the others are zeroes (that is why the PMF is still 1) Since you will sum all terms anyway because they are indistinguishable, you can just use $1= (p + (1-p))^{n}$ for any problem and forget about individual terms because one is arbitrary and the others are $0$
- linear algebra - Can someone please explain what does $ D= P^{-1} AP . . .
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- Why is the variance of a binomial distribution n*p*(1-p)?
I don’t understand why this is the formula for variance for binomial distribution The 1-p especially confuses me The variance in the square of the standard deviation which I don’t get how this gi
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