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Ecuadorian 3-digit numbers - 2019 Ecuador Juniors (OMEC) L2 p1

Source:

October 24, 2022
number theoryDigits

Problem Statement

A three-digit abc‾\overline{abc} number is called Ecuadorian if it meets the following conditions: ∙\bullet abc‾\overline{abc} does not end in 00. ∙\bullet abc‾\overline{abc} is a multiple of 3636. ∙\bullet abc‾−cba‾\overline{abc} - \overline{cba} is positive and a multiple of 3636. Determine all the Ecuadorian numbers.
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