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Find all possible integers

Source: Romanian District Olympiad 2014, Grade 5, P1

June 15, 2014
number theory proposednumber theory

Problem Statement

Find with proof all positive 33 digit integers abc‾\overline{abc} satisfying b⋅ac‾=c⋅ab‾+10 b\cdot \overline{ac}=c \cdot \overline{ab} +10
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