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The answer to the problem described on the 'grrr!' posting explained why I calculated correctly that December 31st 1999 was a Friday but I kept coming up with January 1st 2000 as a Monday. I forgot that the latter date was the first day of the thirteenth month of the last year of the previous century!
But then I tried March 1st 2000:
Remainder: -4 ... So the day was a Thursday, right?
Well, no. It was a Wednesday.
I then tried several other dates in 2000 and noticed that the total has to be a positive number to give an accurate prediction of the day of the week.
It appears that the remainder, when a negative number has to be subtracted from 7 to give the true answer. Is this correct?
Yes, it's conventional in number theory to say that -25 divided by seven is -4 remainder 3. I appreciate this won't be intuitive for everyone, so I'll think up an explanatory footnote.
Thanks for pointing this out!
Forgot to say, the entry's been updated to clarify this.
Hope this is OK.
I think this will help others like me whose maths education didn't run to Number Theory.