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Special Five-digit Positive Integers

Source: 2013 AIME I Problem 2

March 15, 2013
AMCAIMEnumber theorymodular arithmetic2013AIME I

Problem Statement

Find the number of five-digit positive integers, nn, that satisfy the following conditions:
(a) the number nn is divisible by 55, (b) the first and last digits of nn are equal, and (c) the sum of the digits of nn is divisible by 55.
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