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 11 Is $2^{16} = 65536$ the only power of $2$ that has no digit which is a power of $2$ in base-$10$? 10 Prove $\sum_{k=0}^{n}\frac{n!}{k!}(n-k)n^k=n^{n+1}$ for any $n\in\mathbb N$. 7 Find the integer $x$ such $x^6+x^5+x^4+x^3+x^2+x+1=y^3$ 6 How to prove that $a^2b+b^2c+c^2a \leqslant 3$, where $a,b,c >0$, and $a^ab^bc^c=1$ 5 A Sine and Inverse Sine integral

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 14 combinatorics × 4 11 recreational-mathematics 13 algebra-precalculus × 2 11 number-theory 12 inequality × 3 8 diophantine-equations × 3 11 exponentiation 5 trigonometric-series 11 decimal-expansion 5 integration

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