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Number abc in base g will be cba in base h = g ± 1

Source: Austrian Mathematical Olympiad 2003, Part 2, D2, P1

June 18, 2011
number theory proposednumber theory

Problem Statement

Prove that, for any integer g>2g > 2, there is a unique three-digit number abc‾g\overline{abc}_g in base gg whose representation in some base h=g±1h = g \pm 1 is cba‾h\overline{cba}_h.
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