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Three-digit numbers divisible by 4

Source: 2012 AIME I Problem 1

March 16, 2012
modular arithmeticAMCUSA(J)MOUSAMO

Problem Statement

Find the number of positive integers with three not necessarily distinct digits, abcabc, with a≠0a \neq 0, c≠0c \neq 0 such that both abcabc and cbacba are divisible by 4.
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