If $k$ is odd, then $(k-1)k(k+1)$ is divisible by $24$
17965
Prove 24 divides $u^3-u$ for all odd natural numbers $u$
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
155886
let q be an odd prime and p a prime dividing $1+n+\dots+n^{q-1}$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
49509
A number $n$ has $12$ divisors and $d_{d_4-1} = (d_1+d_2+d_4)d_8$.
15631
Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
49501
Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
122534
Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
26503
Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even