Sextalternado numbers
Source: Lusophon Matematical Olympiad 2021 Problem 1
December 19, 2021
number theory
Problem Statement
Juca has decided to call all positive integers with 8 digits as if it is a multiple of 30 and its consecutive digits have different parity. At the same time, Carlos decided to classify all that are multiples of 12 as .a) Show that numbers don't exist.b) Find the smallest number.