Prove that every number has a unique representation in base 3.
48308
Uniqueness of radix representation of integers in base 3
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
149716
Prove that $ \sqrt{n(n+1)(n+2)(n+3)+1} $ is always a natural number
30136
Proof that a Combination is an integer
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
92057
Prove that for every odd integer n, there is a group...
151153
Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$
51653
Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$
23707
How can I prove that every word has unique representation?
91105
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$
33786
Proof that a certain fraction is always an integer
33177
All numbers of form $10^{k} + 1$ are composite for $k{\gt}2$ proof
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
63182
For every $n \ge 1$ there exist uniquely determined integers $a \gt 0$ and $b \gt 0$ such that $n = a^2b$ where $b$ is square-free.
78190
How to prove that for all natural numbers, $4^n > n^3$?
140140
An identity which applies to all of the natural numbers