Tagged Questions
1
vote
6answers
117 views
How to simplify this expression by division
How to divide it
$${\frac {{x}^{n-2}-{y}^{n-2}}{x-y}}$$
to remove the $x-y$ term from the denominator.
We may assume that $n>2$ is an integer.
Thanks.
3
votes
2answers
475 views
Trying to prove that $p$ prime divides $\binom{p-1}{k} + \binom{p-2}{k-1} + \cdots +\binom{p-k}{1} + 1$
So I'm trying to prove that for any natural number $1\leq k<p$, that $p$ prime divides:
$$\binom{p-1}{k} + \binom{p-2}{k-1} + \cdots +\binom{p-k}{1} + 1$$
Writing these choice functions in ...
4
votes
2answers
216 views
Binomial division
Looks very easy, but I can't make it:
$s \geq 2$ and $w \geq 2$ are prime numbers. $k$ is a natural number and $k \leq \min \{s,w \}$
Show that $\binom{s+w}{k}-\binom{w}{k} - \binom{s}{k}$ can be ...
