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sum of digits | n, n+1, n+2, n+3 - All-Russian MO 2001 Regional (R4) 8.6

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September 25, 2024
number theorysum of digits

Problem Statement

We call a natural number nn good if each of the numbers nn, n+1 n+1, n+2n+2 and n+3n+3 are divided by the sum of their digits. (For example, n=60398n = 60398 is good.) Does the penultimate digit of a good number ending in eight have to be nine?
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