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Old 2010-02-17, 20:56   #4
Wacky
 
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Jun 2003
The Texas Hill Country

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Rather than "trying" 3, 8, 13, etc., do it algebraically.

If x = 3 mod 5, then x= 5A+3 for some integer A.
Substituting in the other constraints
5A+3 = 1 mod 3
5A+3 = 2 mod 4

But this is the same as
2A = 1 mod 3
A = 3 mod 4

Thus, we have reduced the number of constraints.
When we find permissible values for A, we can substitute and we will have the permissible values for x
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