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Integer and Number Theoretic Functions
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Reduce
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GCD
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Diophantine Equations
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New in 6.0: Mathematics & Algorithms
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ChineseRemainder
ChineseRemainder
[{
r
1
,
r
2
,
...
}, {
m
1
,
m
2
,
...
}]
gives the smallest positive
x
that satisfies all the integer congruences
x
mod
m
i
=
r
i
mod
m
i
.
MORE INFORMATION
If no solution for
x
exists,
ChineseRemainder
returns unevaluated.
If all
r
i
<
m
i
, then the result satisfies
x
mod
m
i
=
r
i
.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
The smallest positive integer
x
that satisfies
and
:
In[1]:=
Out[1]=
Find the smallest positive integer giving remainder
when divided by
:
In[1]:=
Out[1]=
Applications
(3)
Properties & Relations
(1)
Possible Issues
(1)
SEE ALSO
Reduce
FindInstance
GCD
TUTORIALS
Integer and Number Theoretic Functions
MORE ABOUT
Diophantine Equations
Number Theoretic Functions
Number Theory
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
New in 6
© 2008 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
Applications 