Proof by induction that for every positive integer there is a multiple $m$ for which the digit sum $D(m)=D(m^2)$
87626
Why are all $n$, s.t. the sum of digits of $n$ and $n^2$ coincide, $\equiv 0,1 \bmod 9$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
67527
Proof by Induction that $3^n ≥ 1+2^n$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
94923
Using the Pigeonhole Principle to show that $2$ of any $n+1$ numbers from $\{1,2,\ldots,2n\}$ sum to $2n+1$
33104
Combinatorial Proof with Summation Identity
106416
If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.
3632
Basic number theory proofs
60712
Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
48251
Prove that if $n \in \mathbb{N}$, then $\sum_{d|n}{(d(n))^3}=(\sum_{d|n}{d(n)})^2$ where $d(n)$ is the divisor function.
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
124584
How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
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.
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$