Tagged Questions

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How to find exponent of a number in a combination?

How do I find the exponent of $7$ in $^{100}C_{50}$ that is, $\dfrac{100!}{(100-50)!\cdot 50!} =\dfrac{100!}{50!\cdot 50!}$, this question was out of the blue, and I haven't been able to find any ...
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$2^n$ modulo n where n is odd always yields either an even or $1$

I'm attempting to do a pidgeonhole proof to prove that for some odd integer n, there is always a $2^k$ such that $2^k \mod(n) = 1$. I know that $2^n \mod(n)$ will always yield either an even number or ...
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Rising/Falling Powers, Summation

1) Show that $$(-n)^{\bar p} = (-1)^n n^\underline{p}$$ (original screenshot) 2) Evaluate the sum $$\sum_{a\le n\lt b}n^{\bar p}$$ (original screenshot) Thoughts regarding question 1: I've ...
143 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 ${^n\!P_k}$?
Proof for the uniqueness of all the combination of the digits of $2^k$, where k>3
A long time ago I found a question on the internet that went a little like this: Suppose that we have $n=2^k$ where $k\gt 3$. If $m$ is another number that is a combination of the digits of $2^k$, ...