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• ... Yes, use the Chinese Remainder Theorem: http://mathworld.wolfram.com/ChineseRemainderTheorem.html In fact, you can use a weaker version, if you assume that
Message 1 of 2 , Apr 1, 2005
On Friday 01 April 2005 12:08, you wrote:
> Hello,
>
> I hope this question is germane to this group, and
> reasonable.
>
> Modular arithmetic is also known as clock arithmetic
> therefore my question is:
>
> Given a series of repeating number sequences such as
> a) 012340123401234, b) 012345670123456701234567,
> c) 012345678901234567890123456789, etc., but occurring
> at random intervals such as a) 012340123401234,
> b) 345670123456701234567012,
> c) 789012345678901234567890123456, etc., is there an
> algorithm/formula that would tell me when the 0's, or
> 1's or 2's etc., would line up? Essentially a
> "synchronizing" of the clocks.

Yes, use the Chinese Remainder Theorem:
http://mathworld.wolfram.com/ChineseRemainderTheorem.html

In fact, you can use a weaker version, if you assume that all clocks begin at
the same value but have different periods: the first sync point is at the
beginning, and each subsequent sync point is distanced from the previous by
the least common multiple of the periods of all the clocks.

In general, if each clock has a different starting point, then you'll have to