The system of linear congruence x ≡ a(mod ni) with gcd(ni, nj) = 1 for i ≠ j has a simultaneous solution which is 

1
distinct modulo ni's for 1 ≤ i ≤ ∞  
2
unique modulo ni's for 1 ≤ i ≤ r
3
unique modulo ni's for 1 ≤ i ≤ ∞ 
4
distinct modulo ni's for 1 ≤ i ≤ r

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