Prove that for every integer $x ∈ \mathbb Z$, the number $x^{102} − x^2$ is a multiple of $2020$.
133819
How to prove that $364 \mid n^{91} - n^7$?
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
88051
$\mathbb R = X^2$ as a Cartesian product
151928
How to prove that $N\setminus A$ is finite?
3632
Basic number theory proofs
17176
Proof that $x^n \mod b = (x \mod b)^n$
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
114262
Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
51153
Number of solutions to $x^2\equiv a\pmod m$
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
57746
Prove that, for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
156195
1) Show that $(\Bbb Z[\sqrt2]^*, .)$ is infinite.