Prove $z = \frac {5^{125 }- 1}{5^{25} - 1} $ is composite.
60462
Prove that $\frac{ 5^{125}-1}{ 5^{25}-1}$ is a composite number
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
26501
Proof using complex numbers
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
54059
Showing that $\frac{z^n}{1+z^{2n}}$ is real for $|z|=1$.
147986
Prove: if $|z|=1$ than $\frac{z+1}{z-1}$ is an imaginary number
23694
Given that $abc=1$, prove that $\frac{b}{c} + \frac{c}{a}+ \frac{a}{b} \ge \frac{1}{a} + \frac{1}{b} +\frac{1}{c}$.
79808
Prove the representation of complex numbers is parallelogram
87289
Find the multiplicative inverses of all the elements in $\Bbb Z_{16}^\times$
103803
Prove from first princibles $\frac{x^2-4}{x-4} \rightarrow -5$ as $x \rightarrow 3$
44100
Prove that identity element is unique
112933
Show that $Z\times Z$ is not cyclic...
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$