Number Theory
Factorials
How many of the following 99 integers are primes?
\[\begin{array} &100!+2, &100!+3, &100!+4, &\ldots, &100!+100\end{array}\]
by
Chung Kevin
How many positive integers are divisors of \(21!\) but are not divisors of \(20!\)?
by
Janardhanan Sivaramakr...
Find the remainder when \(70!\) is divided by \(5183\).
Note: Don't use a computational device!
by
Krishna Ar
\[\large \lim_{n \rightarrow \infty} { 2n \choose n } ^ { \frac{1}{n} } = \ ?\]
by
Calvin Lin
How many trailing zeroes are in the decimal representation of \[n=1+\displaystyle{\sum_{k=1}^{2013}k!(k^3+2k^2+3k+1)}?\]
by
Samir Khan