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Repeating decimals (Posted on 2006-09-25) Difficulty: 3 of 5
The decimal expansion of 1/271 repeats with a period of length 5:
.003690036900369 ...

However, it is not the smallest number q for which the decimal expansion of 1/q has a repetition length of 5.

Find the smallest q so that the decimal expansion of 1/q has repetition length n for each of {1, 2, ..., 10}

Is there a simple way of finding such a number?

See The Solution Submitted by Jer    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(2): General solution | Comment 7 of 11 |
(In reply to re: General solution by Jer)

Right, I went for prime numbers, while smaller composite numbers may also produce the same period length.

For example, for D=3: 10^3-1 equals 3^3 times 37; since 3^3<37, 27 is the first number such that 1/27 has a period length of 3.

Edited on September 26, 2006, 12:38 pm
  Posted by Federico Kereki on 2006-09-26 11:34:15

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