Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-08T11:39:09.271Z Has data issue: false hasContentIssue false
  • English
  • Français

On the decimal representation of integers

Published online by Cambridge University Press:  24 October 2008

M. P. Drazin  and
J. Stanley Griffith
M. P. Drazin
Affiliation:
Trinity CollegeCambridge
J. Stanley Griffith
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Let r be any fixed integer with, r≥ 2; then, given any positive integer n, we can find* integers αk(r, n) (k = 0, 1, 2, …) such that

where, subject to the conditions

the integers αk(r, n) are uniquely determined, and, in fact, clearly

αk(r, n) = [n/rk] − r[n/rk+1]

(square brackets denoting integral parts, according to the usual convention).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 4 , October 1952 , pp. 555 - 565
Copyright
Copyright © Cambridge Philosophical Society 1952

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bellman, R. and Shapiro, H. N.On a problem in additive number theory. Ann. Math., Princeton (2), 49 (1948), 333–40.CrossRefGoogle Scholar
(2)Bush, L. E.An asymptotic formula for the average sums of the digits of integers. Amer. math. Mon. 47 (1940), 154–6.Google Scholar
(3)Champernowne, D. G.The construction of decimals normal in the scale of ten. J. Land. math. Soc. 8 (1933), 254–60.Google Scholar
(4)Hardy, G. H. and Wright, E. M.An introduction to the theory of numbers (Oxford, 1945).Google Scholar
(5)Mirsky, L.A theorem on representations of integers in the scale of r. Scr. math., N.Y., 15 (1949), 11–12.Google Scholar
(6)Pillai, S. S.On normal numbers. Proc. Indian Acad. Sci. A, 10 (1939), 13–15.Google Scholar
(7)Pillai, S. S.On normal numbers. Proc. Indian Acad. Sci. A, 12 (1940), 179–84.CrossRefGoogle Scholar