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MMATHS 2021, Problem 2: Digital Reductions

Source:

October 31, 2021
YaleMMATHS

Problem Statement

Define the digital reduction of a two-digit positive integer AB‾\underline{AB} to be the quantity AB‾−A−B\underline{AB} - A - B. Find the greatest common divisor of the digital reductions of all the two-digit positive integers. (For example, the digital reduction of 6262 is 62−6−2=54.62 - 6 - 2 = 54.)
Proposed by Andrew Wu
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