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ChineseRemainder

ChineseRemainder
gives the smallest non-negative x that satisfies all the integer congruences x mod = mod .
MORE INFORMATION
  • If all , then the result satisfies x mod = .
EXAMPLESCLOSE ALL
Basic Examples   (2)
The smallest positive integer x that satisfies and :
Find the smallest positive integer giving remainder when divided by :
The smallest positive integer x that satisfies and :
In[1]:=
Click for copyable input
Out[1]=
 
Find the smallest positive integer giving remainder when divided by :
In[1]:=
Click for copyable input
Out[1]=
Applications   (3)
Database encryption and decryption:
Key generation:
Encrypted data:
Decryption:
Define a residue number system:
Numbers and their representation in a residue system:
Multiplying and recovering in the residue system:
Adding and recovering:
Modular computation of a determinant:
Modular determinants:
Recover result:
Shift residue to be symmetric:
Properties & Relations   (1)
Solve congruential equations using Reduce or FindInstance:
Possible Issues   (1)
Not all congruential equations have a solution:
A solution exists when Mod[ri, GCD[m1, m2, ...]]==Mod[rj, GCD[m1, m2, ...]]:
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