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MC II-A Number Theory Problem 7.6

 
 
HuangBret的头像
MC II-A Number Theory Problem 7.6
HuangBret - 2022年05月8日 Sunday 13:31
 

x = b1c1m2m3 + b2c2m1m3b3c3m1m2.

This is the formula for three equations. Does the same thing work for 4 equations? What about 5? Or 6?



 
LensmireJohn的头像
Re: MC II-A Number Theory Problem 7.6
LensmireJohn - 2022年05月9日 Monday 10:47
 

Good question!

Yes, this same formula extends to prove the result for any number of equations. With N equations there are N terms added up. Each term follows the same pattern with a general $b_i$, $c_i$, and product of all the other mods. I think the general formula makes this more confusing than they actually are, but hopefully the idea makes sense.

Also, to be clear, other than understanding the proof, you do NOT want to use this formula for solving these systems (unless you're writing a computer program or something). It is much easier to solve them directly/recursively looking at two equations at a time.

HuangBret的头像
Re: MC II-A Number Theory Problem 7.6
HuangBret - 2022年06月5日 Sunday 07:21
 

Ok thanks!