Modular Congruence Calculator

About This Tool

Our Modular Congruence Calculator provides a robust solution for solving complex systems of congruences where multiple moduli share a common factor. Designed for students, mathematicians, and cryptography professionals, this tool simplifies the process of finding solutions to congruence equations.

Enter your list of remainders and moduli, then click 'Calculate' to receive the combined solution that satisfies all given conditions. The calculator validates inputs, checks for compatibility, and computes results using an extended Chinese Remainder Theorem approach, accommodating non-coprime moduli.

Beyond basic results, the tool offers step-by-step explanations of how the solution is derived, aiding understanding of the underlying number theory principles. It also provides options to copy, export, or share the results seamlessly. Whether you're solving academic exercises or implementing cryptographic algorithms, this calculator makes modular arithmetic manageable and precise.

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