IMO 1983 LL FIN24

Origin: FIN

Problem

Every x, 0 \leqx \leq1, admits a unique representation x = \infty j=0 aj2−j, where all the aj belong to {0, 1} and infinitely many of them are 0. If b(0) = 1+c 2+c, b(1) = 2+c, c > 0, and f(x) = a0 + \infty  j=0 b(a0) \cdot \cdot \cdot b(aj)aj+1, show that 0 < f(x) −x < c for every x, 0 < x < 1. (FIN 2′) (SL83-11).