Tagged Questions

60 views

Zeta function and probability

I know that $\zeta(n) = \displaystyle\sum_{k=1}^\infty \frac{1}{k^n}$ (Where $\zeta(n)$ is the Riemann zeta function) But the reciprocal of $\zeta(n)$ for $n$ a positive integer is equal to the ...
162 views

Comparing $\large 3^{3^{3^3}}$, googol, googolplex

How to show that $\large 3^{3^{3^3}}$ (Third Ackermann number) is larger than a googol ($\large 10^{100}$) but smaller than googoplex ($\large 10^{10^{100}}$). Thanks much in advance!!!
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Prime decomposition of an integer: methods of determining the prime factors $p_1, p_2, …, p_r$ and powers $k_1,k_2, …, k_r$

Any integer n can be written in the form $n = p_1^{k_1}p_2^{k_2} ... p_r^{k_r}$, where the powers $k_1, k_2, ...,k_r$ are integers and $p_1, p_2, ..., p_r$ are primes. Now I am interested in ...
263 views

Prove that for any nonnegative integer n the number $5^{5^{n+1}} + 5^{5 ^n} + 1$ is not prime

My math teacher gave us problems to work on proofs, but this problem has been driving me crazy. I tried to factor or find patterns in the numbers and all I can come up with is that for $n > 0$, the ...
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Find the greatest powers of $2$ dividing $10!$, $20!$, $30!$, $40!$ [duplicate]

I'm trying to find the greatest powers of $2$ dividing $10!$, $20!$, $30!$, $40!$, as part of a basic number systems course. I'm rather lost with this question. For $10!$ I tried writing the terms ...
149 views

Can we give an upper bound for the sum over primes $p_{i}$ of $\sin(p_{i} x)$?

Let $x$ be a positive real number. Consider the sum $\sum \sin(p_i x)$ taken over all primes $p_i$ from 2 till $n$. Call this function $f(n,x)$. Can we give good upper and lower bounds of $f(n,x)$ ...
106 views

How to find the last non-zero digit in ${^n\!P_k}$?

What is the procedure of finding the last non-zero element in ${^n\!P_k}$?
376 views

Is it known or new? [duplicate]

Possible Duplicate: Starting digits of 2^n While I was randomly working with number patterns, I came along with some interesting pattern which seems to turn to a conjecture in fact. My ...