Showing that, if $n,10$ are coprime, then the last $3$ digits of $n^{101}$ will be the same as $n$'s.
360
Modular exponentiation by hand ($a^b\bmod c$)
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
156786
Show that $15\mid 21n^5 + 10n^3 + 14n$ for all integers $n$.
75685
Prove that there is prime number and natural so $n\times q$ digits are $1$.
112080
Proving the Product Rule for exponents with the same base
119932
Generalizing $\,r(n^2) = r(n)^2,\,$ for $\,r(n) := $ reverse the digits of $n$
128575
Elementary proof that $3$ is a primitive root of a Fermat prime?
105405
Product of three consecutive positive integers is never a perfect power
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
138669
proving that elements of a sequence are pairwise coprime
71789
Prove that the sum of digits of $(999...9)^{3}$ (cube of integer with $n$ digits $9$) is $18n$
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
85941
Proof by induction that $n^3 - n$ is divisible by $6$
23427
How to prove there are no more positive integers that are products of 2 and 3 consecutive numbers?
34767
Proving $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)<3$ for all positive integers $n$