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Guanaco numbers

Source: 2023 Centroamerican and Caribbean Math Olympiad, P4

July 26, 2023
number theory

Problem Statement

A four-digit number n=abcd‾n=\overline{a b c d}, where a,b,ca, b, c and dd are digits, with a≠0a \neq 0, is said to be guanaco if the product ab‾×cd‾\overline{a b} \times \overline{c d} is a positive divisor of nn. Find all guanaco numbers.
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