Waring's problem inequality
One of the oldest (Since 1770) and famous open problem in number theory is Waring's problem. It has been conjectured that if
$$ Frac\bigg[\bigg(\frac{3}{2}\bigg)^n\bigg] \le 1 - \bigg[\bigg(\frac{3}{4}\bigg)^n\bigg]. $$
(where $Frac$ denotes the fractional part) true then, the general solution of Waring's problem is
$$ g(n) = 2^n + Int\bigg[\bigg(\frac{3}{2}\bigg)^n\bigg] - 2. $$
