Show that the cardinal of $ A := \left\{ k \in \mathbf{Z} | 0 \leq k \leq n \text{ and } \binom{n}{k} \text{ is odd} \right\} $ is a power of 2
92166
Number of odd binomial coefficients is a power of $2$
145214
Showing the power set is equinumerous to ${}^X2$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
49066
Give the combinatorial proof of the identity $\sum\limits_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
7843
Show that order of $a^k$
59459
Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
52614
(exercise from Tao's analysis book) Proof of a lemma relating to power set of X
86421
Proof of the definition of cardinal exponentiation
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$