Let $x$ be a whole number. Show that $x(x-1)(x+1)$ divided by $6$ is a whole number.
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
36514
Show that $45<x_{1000}<45.1$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
62732
Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
83407
How to show that that $q \mid p-1$?
85525
Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
74512
How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?
156646
If $x$ is rational then $\,x+\frac{1}x \,$ is an integer $\iff x = \pm 1$
41779
Is $x/x$ equal to $1$
120227
Proving $6^n - 1$ is always divisible by $5$ by induction
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$