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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Powers of two with coefficients {1,−1}
Given a vector $(n_0, n_1, \dots, n_l)$ where $n_i \in \{-1, 1\}$, $i = \overline{0, l-1}, n_l = 1$ and $l \in \mathbb{N}$.
Prove that for all $a$ such that
$$0 < a \leq 2^0\cdot n_0 + 2^1 \cdot n_1 + …