The sum of digits of n and n²

2010/01/23 by K. G. Hare, Hare, K. G., S. Laishram +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1001.4170

16 pages

arxiv created 2010/01/23 · arxiv updated 2010/02/26

Abstract

Let s_q(n) denote the sum of the digits in the q-ary expansion of an integer n. In 2005, Melfi examined the structure of n such that s₂(n) = s₂(n²). We extend this study to the more general case of generic q and polynomials p(n), and obtain, in particular, a refinement of Melfi's result. We also give a more detailed analysis of the special case p(n) = n², looking at the subsets of n where s_q(n) = s_q(n²) = k for fixed k.

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