Chinese Remainder Theorem Solver
Solve a list of integer congruences, including non-coprime moduli when consistent; return the smallest nonnegative solution and its period as exact decimal strings.
Description
Solve a list of integer congruences, including non-coprime moduli when consistent; return the smallest nonnegative solution and its period as exact decimal strings.
Solve a list of integer congruences, including non-coprime moduli when consistent; return the smallest nonnegative solution and its period as exact decimal strings.
When to use Chinese Remainder Theorem Solver
Use this tool to test or transform exact integers according to the named number-theory definition, for education, validation, or algorithm checks.
- residues
- A required input.
- moduli
- A required input.
How the calculation works
Limitations and assumptions
This tool applies an exact integer definition within JavaScript's safe-integer range. It is not an arbitrary-precision factorization or proof system, so do not use rounded measurements or integers beyond the accepted domain as though they were exact.
Alternative or Complementary approaches
Complement a number-property result with its factorization, divisors, digit representation, or a second independent predicate. A true result establishes only the named property and does not imply other properties such as primality.
References
-
Chinese remainder theorem — Wikipedia contributors
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