If $k, m, n$, are natural numbers and $k \leq n$ What is the final answer of this :
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
36694
Sum of first n natural numbers proof
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
147317
multiple choice question on number theory
127843
Prove that, for any natural number $k$ $\exists m \in M $ s.t i) $m$ has exactly $k$ $1$'s, an
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
121694
How to prove $\log n \leq \sqrt n$ over natural numbers?
113342
Confusion of the decidability of $(N,s)$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
117681
For which Natural $n\ge2: \phi(n)=n/2$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
107010
How many elements of order $k$ are in $S_n$?
110383
How many numbers less than $m$ and relatively prime to $n$, where $m>n$?
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$