Re: Number Theory

In article <1149487252.978292.224850@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Proginoskes" <CCHeckman@xxxxxxxxx> wrote:

Gerry Myerson wrote:
In article
<12872806.1149459033916.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Simon Dean <sdean1981@xxxxxxxxx> wrote:

Let me rephrase:

What are the possible remainders when dividing a whole number by 7?

0, 1, 2, 3, 4, 5, and 6.

I am trying to understand why, say, when you divide 1 by 7, your decimal
answer repeats after 6 digits.

In this case, remainder 0 can't happen, and as soon as one of
the other 6 happens a second time, that forces the entire procedure
to repeat, forever. Try it, and see!

That's only part of the answer, since when you divide 1 by 9, the
decimal answer doesn't repeat after 8 digits, but only after 1.

I think the poster means to ask: What are the numbers n which, when you
divide 1 by n, result in a block of (n-1) digits being repeated (and no
blocks of fewer size)? The answer to _that_ is actually a fairly deep
result in Number Theory.

You and I are reading OP's mind in different ways. I took the question
to be, why isn't the period longer than 6; you've taken it to be, why
isn't the period shorter than 6.

Anyway, I don't think the answer to your question is a deep result;
I think it's an open question.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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