How to prove that $2^x,3^x,5^x\in\mathbb N$ implies $x\in\mathbb N$?
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
34154
Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
27147
Proving $n! > n^3$ for all $n > a$
78726
Prove via mathematical induction that $4n < 2^n$ for all $ n≥5$.
156335
Proving Power Set of $\mathbb N$ is Uncountable
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
77973
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
112080
Proving the Product Rule for exponents with the same base
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$