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Romania NMO 2023 Grade 5 P3

Source: Romania National Olympiad 2023

April 14, 2023
number theorysum of digits

Problem Statement

Determine all natural numbers mm and nn such that
nā‹…(n+1)=3m+s(n)+1182, n \cdot (n + 1) = 3^m + s(n) + 1182,
where s(n)s(n) represents the sum of the digits of the natural number nn.
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