If c power of all positive integers is an integer, then c is an integer
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
134352
The number of possible factorizations of a positive integer.
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
33505
Show that every large integer has a large prime-power factor
146439
Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
16660
Prove that any positive number has an $n$th root
16235
Prove by induction that every positive integer is represented by some binary number?
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
41784
Prove using mathematical induction that $n < 3 ^n$ for all positive integers n.
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
63300
Product of Consecutive Integers is Not a Power
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
145397
How to prove that for every $i$, $a_i = i$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
56985
Show that every positive integer has a unique representation in the form $50k+l$...?