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smallest n so that r =\overline{a_1a_0a_m ..._20} = 2n, in decimal

Source: Mexican Mathematical Olympiad 1989 OMM P4

July 27, 2018
number theorydecimal representation

Problem Statement

Find the smallest possible natural number n=am...a2a1a0‾n = \overline{a_m ...a_2a_1a_0} (in decimal system) such that the number r=a1a0am...20‾r = \overline{a_1a_0a_m ..._20} equals 2n2n.
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