$S \subset \mathbb{Z}$ where $|S|=n$ and $n \ge 3$. Show $\exists \ x ,y \in S$ distinct with $x-y \equiv 0 \mod n-1$
127069
Discrete Math - Counting
151928
How to prove that $N\setminus A$ is finite?
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
154494
Prove that there exists a row or a column of the chessboard which contains at least √n distinct numbers.
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
158882
Prove the existence of some weird family of sets
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
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.
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
99630
For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
144164
If $x,y,z>0$ are distinct and $x+y+z=1$ what is the minimum of $\left((1+x)(1+y)(1+z)\right)/\left((1-x)(1-y)(1-z)\right)$?
23097
Prove that every number ending in a $3$ has a multiple which consists only of ones.
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.