Show for all integers $n$, if $d$ is an integer such that $d|(n+5)$ and $d|(n^2+7)$, then $d|32$
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
150185
Let $d=GCD(n^2+5,n^3-5n^2+6n)$ show that $d|630$
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
53937
Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$.
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
48622
Given an integer $a$, suppose $d=\gcd(3a+5,\,5a+7)>2$. Determine $d$.
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
120290
Probability that $7^m+7^n$ is divisible by $5$
90806
Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
52032
Prove that ${n^5 - n}$ is divisible by 5
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
95141
$n^5-n$ is divisible by $10$?