Prove that given number is integer
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
97684
Show $\frac{(2n)!}{n!\cdot 2^n}$ is an integer for $n$ greater than or equal to $0$
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
11470
Divisibility of integers
156646
If $x$ is rational then $\,x+\frac{1}x \,$ is an integer $\iff x = \pm 1$
123296
Determine whether a number is prime
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
119278
The number $\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^n\right]$ is always an integer
45460
Proof verification of a number theory problem involving sequences.
42285
Prove by mathematical induction.
126945
checking if a number is a prime
10744
Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3
51408
Converting numbers to integers
101899
Proof By Induction of a Sum
73020
Every integer is congruent to the sum of its digits mod 9