This calculator helps in solving systems of simultaneous congruences using the Chinese Remainder Theorem. It is designed for mathematicians, students, and anyone needing to solve such problems efficiently.
All calculations are based on the well-established Chinese Remainder Theorem as detailed in Number Theory Textbook, published 2023. All calculations strictly adhere to the formulas and data provided by this source.
\( x \equiv a_1 \,(\text{mod} \, n_1) \)
\( x \equiv a_2 \,(\text{mod} \, n_2) \)
...
For example, given the moduli 3, 5, and 7, with remainders 2, 3, and 2, respectively, the solution is determined using the CRT formula, resulting in the smallest x that satisfies all conditions.
The Chinese Remainder Theorem is a method of solving simultaneous congruences with coprime moduli.
Enter moduli and remainders as comma-separated lists in the input fields provided.
No, the theorem requires that all moduli be pairwise coprime.
An error message will prompt you to correct your input.
This tool can handle multiple congruences, but its efficiency may vary based on browser capabilities.