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last four digits in base 2 are the same as its last four digits in base 5

Source: 2019 Dürer Math Competition Finals Day2 E+14 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
number theorylast digitsDigits

Problem Statement

Let SS be the set of all positive integers less than 10,00010,000 whose last four digits in base 22 are the same as its last four digits in base 55. What remainder do we get if we divide the sum of all elements of SS by 1000010000?
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