Prove that $(2+ \sqrt5)^{\frac13} + (2- \sqrt5)^{\frac13}$ is an integer
7066
Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
143510
Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
60462
Prove that $\frac{ 5^{125}-1}{ 5^{25}-1}$ is a composite number
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
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
41418
$2+2 = 5$? error in proof
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
50599
Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
108504
Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
31245
How to prove that Fibonacci number is integer?
26606
Prove the inequality $\,\frac{1}{\sqrt{1}+ \sqrt{3}} +\frac{1}{\sqrt{5}+ \sqrt{7} }+\ldots+\frac{1}{\sqrt{9997}+\sqrt{9999}}\gt 24$
24301
Can a finite sum of square roots be an integer?
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 $x-1$