How many positive integral values of $n$, less than $100$, are there such that $n^3+72$ is completely divisible by $n+7$?
30261
How can I find all integers $x≠3$ such that $x−3|x^3−3$
120290
Probability that $7^m+7^n$ is divisible by $5$
27069
sum of all positive integers less than $n$ and relatively prime to $n$
141073
Are there fewer positive integers than all integers?
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
91451
find all positive integer $m,n$
137808
$n^2 + 3n +5$ is not divisible by $121$
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
105405
Product of three consecutive positive integers is never a perfect power
50940
Prove $1^{2007}+2^{2007}+\cdots+n^{2007}$ is not divisible by $n+2$
44409
Number of Elements Not divisble by 3 or 5 or 7
60284
Infinitely many positive integers $n$ such that $\phi(n) = \frac{n}{4}$?
116970
On the number divisors of a number
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
153892
Number Theory divisibilty
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws