# university 1st yr algebra--congruence

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• November 3rd 2008, 01:35 PM
pnyfat
university 1st yr algebra--congruence
coulld anybody help me with this one? thx so much!
or just show me the method, copying me any useful website to look it up...all sorts of help will be thanked!

determine is the congruence has solution, if does determine the complete solution.

http://www.mathhelpforum.com/math-he...ruence-mod.gif

thankssssss
• November 3rd 2008, 01:53 PM
BoboStrategy
Congruence
a $\equiv$ b (mod c)

means that c divides a - b

In this context, "c divides a - b" means there is an integer t so that c*t = a-b.

In your example,

1713x $\equiv$ 851 (mod 2000)

means find x so that 2000 divides 1713x - 851.

One such x is 227.
• November 3rd 2008, 07:24 PM
pnyfat
Quote:

Originally Posted by BoboStrategy
a $\equiv$ b (mod c)

means that c divides a - b

In this context, "c divides a - b" means there is an integer t so that c*t = a-b.

In your example,

1713x $\equiv$ 851 (mod 2000)

means find x so that 2000 divides 1713x - 851.

One such x is 227.

thank you very much for the "227".
however what i am trying to dig out from this problem is how to do this kind of question in steps, but not getting the English meaning of it and figure out a number which seems meaningless to me.