HMMT November 2015 U35

Guts
Answer

Let $n$ be the smallest positive integer such that any positive integer can be expressed as the sum of $n$ integer 2015th powers. Find $n$ . If your answer is $a$ , your score will be $\max \left(20-\frac{1}{5}\left|\log _{10} \frac{a}{n}\right|, 0\right)$ , rounded up.

Dataset text NuminaMath olympiads. Quoted with source.

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2^{2015}+\left\lfloor\left(\frac{3}{2}\right)^{2015}\right\rfloor-2

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