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Frank

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earned this badge 9 times.

How to find all naturals $n$ such that $\sqrt{1 {\underbrace{4\cdots4}_{n\text{ times}}}}$ is an integer?

Awarded Sep 14, 2017 at 19:19

Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$

Awarded Feb 2, 2016 at 10:06

Integral:$ \int^\infty_{-\infty}\frac{\ln(x^{2}+1)}{x^{2}+1}dx $

Awarded Oct 28, 2014 at 9:52

Finding all integers such that $a^2+4b^2 , 4a^2+b^2$ are both perfect squares

Awarded Aug 23, 2012 at 9:01

proving :$\frac{ab}{a^2+3b^2}+\frac{cb}{b^2+3c^2}+\frac{ac}{c^2+3a^2}\le\frac{3}{4}$.

Awarded Aug 15, 2012 at 19:50

Evaluating :$\int \frac{1}{x^{10} + x}dx$

Awarded Jul 17, 2012 at 21:59

Finding all primes $p$ such that $\frac{(11^{p-1}-1)}{p}$ is a perfect square

Awarded Jul 14, 2012 at 7:05

Prove that there does not exist any positive integers pair $(m, n)$ satisfying: $n(n + 1)(n + 2)(n + 3) = m{(m + 1)^2}{(m + 2)^3}{(m + 3)^4}$

Awarded Jul 10, 2012 at 20:06

Proving that there exists $a_i \in \{a_1,\dots,a_k\}$ so that for any positive integer $n$ $F(n)$ is divisible by $a_i$

Awarded Jul 6, 2012 at 15:14

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