Let $n\in\Bbb Z$. Prove that $n$ is a multiple of both $5$ and $9$ if and only if it is a multiple of $45$.
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
95669
Solutions of $|z| = z^5$ in $\Bbb{C}$?
103545
Prove "casting out nines" of an integer is equivalent to that integer modulo 9
27449
Product of Divisors of some $n$ proof
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
43010
Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.
41571
Prove that in a sequence of numbers $49 , 4489 , 444889 , 44448889\ldots$
141531
Find the set of $n\in\Bbb Z^+$ with $M=\{n,n+1,n+2,n+3,n+4,n+5\}$ partitionable into two sets
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
125040
Show by induction : $n^7-n$ is a multiple of 7
115284
For $5$ distinct integers $a_i$, $1\le i\le5$, $f(a_i)=2$. Find an integer b (if it exists) such that f(b) = $9$.
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N
98963
Prove that neither $A$ nor $B$ is divisible by $5$
146867
Combinatorial Proof Of A Number Theory Theorem--Confusion