For a positive integer \( n \), let \( S(n) \) be the sum of all decimal digits in \( n \), i.e., if \( n = n_1 n_2 \dots n_m \) is the decimal expansion of \( n \), then \( S(n) = n_1 + n_2 + \dots + n_m \). Find all positive integers \( n \) and \( r \) such that \( (S(n))^r = S(n^r) \).
Tag Archives: digit
2017-06 Powers of 2
Does there exist infinitely many positive integers \(n\) such that the first digit of \(2^n\) is \(9\)?