Let $S(k)$ denote the digit-sum of a positive integer $k$(in base $10$). Determine the smallest positive integer $n$ such that \[S(n^2 ) = S(n) - 7\]
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Tags: modular arithmetic, number theory unsolved, number theory
Let $S(k)$ denote the digit-sum of a positive integer $k$(in base $10$). Determine the smallest positive integer $n$ such that \[S(n^2 ) = S(n) - 7\]