Prove that there is an integer $k$ such that $2^k$ is starting with $999$
51680
decimal representation of $2^m$ starts with a particular finite sequence of decimal digits
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
45460
Proof verification of a number theory problem involving sequences.
36639
Prove by induction that $\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$
127843
Prove that, for any natural number $k$ $\exists m \in M $ s.t i) $m$ has exactly $k$ $1$'s, an
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
125707
A simple proof (hopefully) for $2^x \neq 0$
46102
Prove that $2^n +1$ in never a perfect cube
62177
Prove that: $2^n < n!$ Using Induction
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
1409
Proving that the given set has at most $2^{n-1}$ elements
34154
Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.
110635
Proving $\mathbb{N}^k$ is countable
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
24954
Prove that there are infinitely many integers of the form $111\ldots111$ that are multiple of $n$.
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
94575
Inductive proof that there are infinitely many pairs of consecutive powerful integers?