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$$Frac\bigg[\bigg(\frac{3}{2}\bigg)^n\bigg] \le 1 - \bigg[\bigg(\frac{3}{4}\bigg)^n\bigg].$$
(where $Frac$ denotes the fractional part) true then, the general solution of Waring's problem is
$$g(n) = 2^n + Int\bigg[\bigg(\frac{3}{2}\bigg)^n\bigg] - 2.$$