"Let n1, n2,...nr be a positive integers such that gcd(ni, nj)=1 for i not equal to j. Then the system of linear congruences;

x= a1 (mod n1)
x=a2 (mod n2)
.
.
x=ar (mod nr)

has a simultaneous solution, which is unique modulo the integer n1n2...nr"

help please . verify what the theorem implies. . please. .

Question

"Let n1, n2,...nr be a positive integers such that gcd(ni, nj)=1 for i not equal to j. Then the system of linear congruences; 

x= a1 (mod n1) 
x=a2 (mod n2)
 . 
 . 
x=ar (mod nr) 

has a simultaneous solution, which is unique modulo the integer n1n2...nr"

help please . verify what the theorem implies. . please. .

anonymous · Answer

Obligatory post, so I can be reminded when someone answers the question.

anonymous · Answer

The theorem you stated above is called the Chinese remainder theorem, which is an important theorem in number theory. Here's a good proof for it. http://www.proofwiki.org/wiki/Chinese_Remainder_Theorem

anonymous · Answer

what anwara said
crt has many uses.

anonymous · Answer

hi ffm
is this your post?

anonymous · Answer

yeah, what sat and anwar said, this problem is just asking for CRT application, and the proof itself is the proof of CRT.

anonymous · Answer

Hi sat, what do you mean?

anonymous · Answer

i thought you made an another alias.

anonymous · Answer

be rational
get real 
same as yours

anonymous · Answer

lol, no I never mad any alias other than FoolForMath, aha! that's a coincidence

anonymous · Answer

But you have to agree that blue is cuter

anonymous · Answer

yes it is better. anyway turns ouit jerwyn gayo is some guy named.... jerwyn gayo http://www.facebook.com/people/Jerwyn-Gayo/100001326383854

anonymous · Answer

lol, haha. do you know about me to?

anonymous · Answer

too*

anonymous · Answer

no

anonymous · Answer

but it always amazes me (i am old) how damn quick it is to get information about people.
go to their profile, and they post there names and schools etc.  quick google search and you get all kinds of things.

anonymous · Answer

yeah it's easy to trace people these days.

anonymous · Answer

not just facebook page. all kinds of photos etc.

anonymous · Answer

when my identity is revealed i will disappear forever...

anonymous · Answer

lol, I know what you mean, let me try tracing you :P

anonymous · Answer

go ahead. let me know what you find

anonymous · Answer

lol, nothing, seems like sat73 don't use anything except OS

anonymous · Answer

if you google "satellite73" images you get some guy who lives in portland. that is not me

anonymous · Answer

I tried "satellite73 math"

anonymous · Answer

http://www.okcupid.com/profile/satellite73 last time i wore a knit cap my mother made me wear it and i was embarrassed

anonymous · Answer

lol

anonymous · Answer

@everyone. .  can anybody tells me what does "ni , nj" implies in the theorem?