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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
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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

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References

REFERENCES

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