What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power? 
What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?

I have tried multiplying every perfect square (up to 400 by two and checking if it is a perfect 5th power, but still nothing. I don't know what to do at this point.

Hint: Let the required number be x:
$\frac{1}{2}x= A^2$
$\frac{1}{5}x= B^5$
$\frac{1}{2}x+\frac{1}{5}x =A^2+B^5$
$\frac{5x+2x}{10}=A^2+B^5$
$7x=10(A^2+B^5)$
⇒ $x=10k$; $k ∈ N  $.
So x is a power of 10.
The smallest 5th power of 10 is $10^5$ so the number must be $5\times 10^5=500000$.
