Modulo Operations with Negative Numbers

Calculates the remainder of a division operation when negative numbers are involved, providing accurate results based on modular arithmetic principles. Users input two integers—a dividend and a divisor—and the tool determines the unique smallest non-negative integer that is congruent to the given inputs modulo the divisor. It handles various combinations of signs, ensuring consistent and mathematically correct outputs for operations like $a \pmod n$ where $a$ or $n$ may be negative. This utility serves students and professionals studying number theory, abstract algebra, or cryptography who require precise calculations involving modular congruences. Individuals needing to solve complex equations or verify properties related to cyclic groups can use this resource.