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

*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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## Cite this paper

Choi, J. Y. (2019). Indispensable digits for digit sums. *Notes on Number Theory and Discrete Mathematics*, 25(2), 40-48, DOI: 10.7546/nntdm.2019.25.2.40-48.