The sum of digits of n and n^2
La somme des chiffres de n et n^2
Résumé
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 s_2 (n) = s_2 (n^2). 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) = n^2 , looking at the subsets of n where s_q (n) = s_q (n^2) = k for fixed k.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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