How Do I solve This?

**kap** · March 30th 2010, 10:56 AM

Hi everyone,

I am trying to find all the solutions for the following system :

$ x \equiv 1 (mod 2) \\ x \equiv 2 (mod 3) \\ x \equiv 3 (mod 5) \\ x \equiv 5 (mod 7) $

[All the x's begin with new line. I'm finding it hard to include newlines that is why.]
I learnt it follows the following pattern:

$ x = a_{1}M_{1}y_{1} + a_{2}M_{2}y_{2} + a_{3}M_{3}y_{3} + a_{4}M_{4}y_{4} $

My problem now is how to find the M's and the y's. I am finding it hard to calculate the M's and the y's.

I need some explanation to solve it.

Thanks for your help.

**tonio** · March 30th 2010, 01:52 PM

Originally Posted by kap

Hi everyone,

I am trying to find all the solutions for the following system :

$ x \equiv 1 (mod 2) \\ x \equiv 2 (mod 3) \\ x \equiv 3 (mod 5) \\ x \equiv 5 (mod 7) $

[All the x's begin with new line. I'm finding it hard to include newlines that is why.]
I learnt it follows the following pattern:

$ x = a_{1}M_{1}y_{1} + a_{2}M_{2}y_{2} + a_{3}M_{3}y_{3} + a_{4}M_{4}y_{4} $

My problem now is how to find the M's and the y's. I am finding it hard to calculate the M's and the y's.

I need some explanation to solve it.

Thanks for your help.

Google "Proof of Chinese Remainder Theorem"

Tonio

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