Show that $A = \{p\in\mathbb{ Q}^+\mid p^22\}$ contains no smallest number
4552
Choice of $q$ in Baby Rudin's Example 1.1
44076
Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$
90537
Converse of Fermat's Little Theorem.
81346
Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
21986
What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
64148
If $p$ and $q$ are distinct primes and $a$ be any integer then $a^{pq} -a^q -a^p +a$ is divisible by $pq$.
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.
50019
Prove $0$ is a partial limit of $a_n$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
133481
How to find the smallest number with just $0$ and $1$ which is divided by a given number?
27889
If the set of odd numbers is a subset of $\mathbb N$ then surely it is smaller than $\mathbb N$
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.