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How many good integers are there?

Source: Excursion

June 25, 2020
number theoryDivisibilitypositive integer

Problem Statement

Let NN be a ten digit positive integer divisible by 77. Suppose the first and the last digit of NN are interchanged and the resulting number (not necessarily ten digit) is also divisible by 77 then we say that NN is a good integer. How many ten digit good integers are there?
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