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Martin Sleziak
Martin Sleziak
11:26 AM
Now those two question I've mentioned above are closed in the other direction.
 
 
1 hour later…
Martin Sleziak
Martin Sleziak
12:27 PM
It seems that we have plenty of copies of this question:
6
Q: How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$

agustinhow to prove: $$ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$$ $\prod_{d|n} d$ is product of all of distinct positive divisor of $n$, $\tau (n)$ is number (count)of all of positive divisor of $n$

elementary-number-theory arithmetic-functions divisor-counting-function
3
Q: What does the product of all proper divisors equal to?

ChanI'm looking for a formula to calculate the product of all proper divisors of a number number $n$. Any idea? Thanks, Chan

elementary-number-theory
0
Q: Product of all divisors

user67427 Prove that $\prod_{d \mid n}d=n^{v(n)/2}$ where $v(n)$ is the sum of divisors function. We have if $n=p_{1}^{a_{1}}p_{2}^{a_{2}} \dots p_{k}^{a_{k}}$ then $v(n)=(a_{1} +1)(a_{2}+1) \dots (a_{k} +1)$ substituting this in the expression does not reach anything, is there any way to express $\p...

elementary-number-theory arithmetic-functions divisor-counting-function
2
Q: How to show that $\prod_{d/n} d = n^{\frac{\tau(n)}{2}}$

Jearson Narvaez Rojasset $ n, n \in \mathbb{N}$ and prove that $\prod_{d/n} d = n^{\frac{\tau(n)}{2}}$ ¨I have tried this¨ If $n > 1$ then $n = p_{1}^{\alpha_{1}}\cdot p_{2}^{\alpha_{2}}\cdots p_{k}^{\alpha_{k}}$ so $n^{\frac{\tau(n)}{2}}=(p_{1}^{\alpha_{1}}\cdot p_{2}^{\alpha_{2}}\cdots p_{k}^{\alpha_{k}})^{...

elementary-number-theory arithmetic-functions divisor-counting-function
 

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