Ancient war trickery is alive in math today
quantamagazine.org
Ancient war trickery is alive in math today
1–10 of 26 posts
Re: Ancient war trickery is alive in math today
#2I never heard of this during my university days. Or maybe I did, and I’ve just forgotten about it. But it’s really nice piece of math, and quiet useful.
Last year’s Advent of Code had a problem that could be solved quickly using this.
Re: Ancient war trickery is alive in math today
#3I never heard of this during my university days. Or maybe I did, and I’ve just forgotten about it. But it’s really nice piece of math, and quiet useful. Last year’s Advent of Code had a problem that could be solved quickly using this.
Most courses in abstract algebra would cover this.
Re: Ancient war trickery is alive in math today
#4> “If there are no solutions modulo a prime, then you know there are no solutions,”
Can anyone point me towards a proof of this?
Re: Ancient war trickery is alive in math today
#5> “If there are no solutions modulo a prime, then you know there are no solutions,” Can anyone point me towards a proof of this?
If there are solutions, they work modulo any prime.
Re: Ancient war trickery is alive in math today
#6> “If there are no solutions modulo a prime, then you know there are no solutions,” Can anyone point me towards a proof of this?
[deleted]
Re: Ancient war trickery is alive in math today
#7> “If there are no solutions modulo a prime, then you know there are no solutions,” Can anyone point me towards a proof of this?
Assume there is a solution to the equation. Then if you take the mod n of both sides the new equality will also hold, for any n. Therefore, if you can prove there are no solution for the mod n equation, then the original equation is also not solvable. This of course also hold when n is prime.
Re: Ancient war trickery is alive in math today
#8I never heard of this during my university days. Or maybe I did, and I’ve just forgotten about it. But it’s really nice piece of math, and quiet useful. Last year’s Advent of Code had a problem that could be solved quickly using this.
in Tunisia, this is covered by highschool seniors in the math section.
Re: Ancient war trickery is alive in math today
#9> “If there are no solutions modulo a prime, then you know there are no solutions,” Can anyone point me towards a proof of this?
The wikipedia page is rather comprehensive:
https://en.wikipedia.org/wiki/Chinese_remainder_theorem
It also covers the straightforward generalization of the theorem to principal ideal domains (e.g. polynomials over a field)
Re: Ancient war trickery is alive in math today
#10I never heard of this during my university days. Or maybe I did, and I’ve just forgotten about it. But it’s really nice piece of math, and quiet useful. Last year’s Advent of Code had a problem that could be solved quickly using this.
CRT is one of the core results of elementary number theory. Elementary number theory is arguably one of the two most axiomatic and most beautiful branches of elementary mathematics, the other being Euclidean geometry. It is, in my opinion, the best pedagogical subject to teach mathematical thinking, and should be taught to more middle schoolers / high schoolers. Unfortunately, I don’t think it will work in places where most middle school / high school teachers themselves have abysmal understanding of mathematics and can only teach you to recite shit or plug numbers into formulae.