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But its application to counting troops... well, this sounds like a really overdone method of doing this. Maybe it has been tried once or twice, but I guess it's probably more of an urban legend, than something that could be pragmatically used on a daily basis.
Well, this is the kind of result you get if you insist on referring to people by the combination of a common last name and a standard courtesy title. Imagine if we referred to the author of The Wealth of Nations as "Mr. Smith" instead of "Adam Smith".
> “If there are no solutions modulo a prime, then you know there are no solutions,” Can anyone point me towards a proof of this?
You can find a similar statement as "Proposition 3.2.2" in Chapter 3 "Modular Arithmetic" [1] of this introductory course [2] to Number Theory. Here is a picture of the statement [3].
Basically, if there exists a number n such that there is no solution modulo n, then you know there are no solutions. Here is a simple application [4] of the proposition with n = 2 and 3.
[1] http://www2.math.ou.edu/~kmartin/intro-nt/ch3.pdf> [2] http://www2.math.ou.edu/~kmartin/intro-nt/>
[3] https://i.ibb.co/8mNHW0Q/2021-09-20-10-34-25.png> [4] https://i.ibb.co/Qffr9k2/2021-09-20-10-56-29.png>
I've read about it many years ago, possibly in some book about cryptography, maybe. AFAIR it's used in some algos in this field. But its application to counting troops... well, this sounds like a really overdone method of doing this. Maybe it has been tried once or twice, but I guess it's probably more of an urban legend, than something that could be pragmatically used on a daily basis.
> the Chinese mathematician Sun Tzu (not to be confused with Sun Tzu who wrote The Art of War almost 1,000 years earlier). Well, this is the kind of result you get if you insist on referring to people by the combination of a common last name and a standard courtesy title. Imagine if we referred to the author of The Wealth of Nations as "Mr. Smith" instead of "Adam Smith".
https://en.m.wikipedia.org/wiki/Adam_Smith_(disambiguation)
They should all use use a unique hanzi name or an ORCID or a UUID or something.
> the Chinese mathematician Sun Tzu (not to be confused with Sun Tzu who wrote The Art of War almost 1,000 years earlier). Well, this is the kind of result you get if you insist on referring to people by the combination of a common last name and a standard courtesy title. Imagine if we referred to the author of The Wealth of Nations as "Mr. Smith" instead of "Adam Smith".
"Clever use of the Chinese Remainder Theorem allows for splitting the computation into 9 independent parts, each computing L19 modulo 2^64 minus some small number, contributing 64 bits of the 566 bit result."
> the Chinese mathematician Sun Tzu (not to be confused with Sun Tzu who wrote The Art of War almost 1,000 years earlier). Well, this is the kind of result you get if you insist on referring to people by the combination of a common last name and a standard courtesy title. Imagine if we referred to the author of The Wealth of Nations as "Mr. Smith" instead of "Adam Smith".
Writing the tones could help a lot as it basically multiplies the number of possible names by 5 per character, so for 3 character names (which seem common in China) we get 125 fold increase in the possible names.
It's not going to help much in general, because Chinese family names just aren't that diverse.
> the Chinese mathematician Sun Tzu (not to be confused with Sun Tzu who wrote The Art of War almost 1,000 years earlier). Well, this is the kind of result you get if you insist on referring to people by the combination of a common last name and a standard courtesy title. Imagine if we referred to the author of The Wealth of Nations as "Mr. Smith" instead of "Adam Smith".
Imagine referring to someone by common first name found by flicking through the first pages of the bible, and then a a reference to a vague class of ubiquitous professions. https://en.m.wikipedia.org/wiki/Adam_Smith_(disambiguation) They should all use use a unique hanzi name or an ORCID or a UUID or something.