On Some Properties of Digital Roots


Digital roots of numbers have several interesting properties, most of which are well-known. In this paper, our goal is to prove some lesser known results concerning the digital roots of powers of numbers in an arithmetic progression. We will also state some theorems concerning the digital roots of Fermat numbers and star numbers. We will conclude our paper by an interesting application.

Share and Cite:

Izmirli, I. (2014) On Some Properties of Digital Roots. Advances in Pure Mathematics, 4, 295-301. doi: 10.4236/apm.2014.46039.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] O’Beirne, T.H. (1961) Puzzles and Paradoxes. New Scientist, No. 230, 53-54
[2] Gardner, M. (1987) The Second Scientific American Book of Puzzles and Diversions. University of Chicago Press, Chicago.
[3] Trott, M. (2004) The Mahematica Guide Book for Programming. Springer-Verlag, New York.
[4] Ghannam, T. (2012) The Mystery of Numbers: Revealed through Their Digital Roots. 2nd Edition, Create Space Publications, Seattle.
[5] Dudley, U. (1978) Elementary Number Theory. Dover, New York.
[6] Pritchard, C. (2003) The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching. Cambridge University Press, Cambridge.
[7] Hinden, H.J. (1974) The Additive Persistence of a Number. Journal of Recreational Mathematics, 7, 134-135.
[8] Averbach, B. and Orin, C. (2000) Problem Solving through Recreational Mathematics. Dover Publications, Mineola.
[9] Polya, G. (1957) How to Solve It: A New Aspect of Mathematical Method. 2nd Edition, Princeton University Press, Princeton.
[10] Noller, R.B., Ruth, E.H. and David, A.B. (1978) Creative Problem Solving in Mathematics . State University College at Buffalo, Buffalo.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.