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Let q ≥ 2 and denote by sq the sum-of-digits function in base q. For j = 0, 1, . . . , q − 1 consider #{0 ≤ n < N : sq(2n) ≡ j (mod q)}. In 1983, F. M. Dekking conjectured that this quantity is greater than N/q and, resp...