Interesting Esoterica

A Theorem On Repeating Decimals

Article by William G. Leavitt
  • Published in 1967
  • Added on
In the collection
In the following, we will develop from the beginning the theory of repeating decimals. This is to provide the necessary machinery for the proof of Midy's theorem, as well as for completeness.

Comment

Midy's theorem: when the repeating part of the reciprocal of a prime number has an even number of digits, the first half and the second half, interpreted as integers, add up to 999...999.

Links

Other information

key
ATheoremOnRepeatingDecimals
type
article
date_added
2025-08-28
date_published
1967-09-26

BibTeX entry

@article{ATheoremOnRepeatingDecimals,
	key = {ATheoremOnRepeatingDecimals},
	type = {article},
	title = {A Theorem On Repeating Decimals},
	author = {William G. Leavitt},
	abstract = {In the following, we will develop from the beginning the theory of repeating decimals. This is to provide the necessary machinery for the proof of Midy's theorem, as well as for completeness.},
	comment = {Midy's theorem: when the repeating part of the reciprocal of a prime number has an even number of digits, the first half and the second half, interpreted as integers, add up to 999...999. },
	date_added = {2025-08-28},
	date_published = {1967-09-26},
	urls = {https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1047{\&}context=mathfacpub},
	collections = {fun-maths-facts},
	url = {https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1047{\&}context=mathfacpub},
	year = 1967,
	urldate = {2025-08-28}
}