If $a+b$ is even, then $24|ab(a^2-b^2)$
49711
Prove that $6p$ is always a divisor of $ab^{p} - ba^{p}$.
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
40274
If $|a| = 12, |b| = 22$ and $\langle a \rangle\cap \langle b\rangle \ne e$, prove that $a^6 = b^{11}$
138890
Cool property of the number $24$
40269
Proving if $x^3$ is even, then $x$ is even.
105985
Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
113168
If $a > b$, is $a^2 > b^2$?
6096
If $A+B=AB$ then $AB=BA$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
20691
prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
32803
Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$