Prove that for every integer $n \geq 0$, the number $4^{2n+1}+3^{n+2}$ is a multiple of 13.
53162
$13\mid4^{2n+1}+3^{n+2}$
60738
If 4n+1 and 3n+1 are both perfect sqares, then 56|n. How can I prove this?
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
153123
Proving by induction $4^n  0$
1895
How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
120309
Number Theory Inequality Proof
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
77091
Inequality $\binom{2n}{n}\leq 4^n$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$
78190
How to prove that for all natural numbers, $4^n > n^3$?
22023
Infinitely number of primes in the form $4n+1$ proof
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$