MathDB
2AB=\overline{AB}

Source: 2021 Taiwan APMO Preliminary First Round

November 21, 2020
number theory

Problem Statement

Find all positive integers A,BA,B satisfying the following properties: (i) AA and BB has same digit in decimal. (ii) 2⋅A⋅B=AB‾2\cdot A\cdot B=\overline{AB} (Here ⋅\cdot denotes multiplication, AB‾\overline{AB} denotes we write AA and BB in turn. For example, if A=12,B=34A=12,B=34, then AB‾=1234\overline{AB}=1234)
Back to ProblemsView on AoPS