Indispensable digits for digit sums

Ji Young Choi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 40-48
DOI: 10.7546/nntdm.2019.25.2.40-48
Full paper (PDF, 181 Kb)

Details

Authors and affiliations

Ji Young Choi

Department of Mathematics, Shippensburg University of PA
1871 Old Main Dr., Shippensburg PA 17257, United States

Abstract

Let b be an integer greater than 1 and g = b − 1. For any nonnegative integer n, we define indispensable digits in the base-b representation of n so that we can calculate the digit sum of the base-b representation of g · n: Instead of adding every digit in it, we multiply g by the number of the indispensable digits in the base-b representation of n. Then, we find the formula to calculate the digit sum of g · n + r using the number of indispensable digits in n, for any nonnegative integers n and r with 0 < r < g.

Keywords

• Digit sum
• Indispensable digits
• Digit sum congruence
• Casting out nines
• Divisibility test

2010 Mathematics Subject Classification

• 11A63
• 11A07

References

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