Using the pigeonhole principle prove that the decimal expansion of $1/k$ for any $k\in\Bbb N_{>0}$ becomes cyclic at some point
46561
How can I prove that all rational numbers are either terminating decimal or repeating decimal numerals?
20135
Measure of  reals in $[0,1]$ which don't have $4$ in decimal expansion
30523
A binary irrational with bits defined by primes
151935
Proving the predicate $\forall n \in \mathbb{N} , n \geq 2$ using the Pigeonhole principle
94295
Pigeonhole-principle with two choices
23076
Proof of limit of quotient sequence property
31867
Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational
13906
How to prove the set $S$ is closed under the binary operation $a*b=a+b+kab$?
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
33786
Proof that a certain fraction is always an integer
101804
Problem concerning the use of Pigeonhole (Box) principle
103606
Proof of sandwich/squeeze theorem for series.
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
69046
Proof of $\mathbb{Q}$ is not cyclic
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
66019
Revisited: Binomial Theorem: An Inductive Proof
90537
Converse of Fermat's Little Theorem.