Modulo calculator

The three conventions disagree only when a is negative, which is the whole lesson: JavaScript, Java, and C truncate toward zero so the remainder takes the sign of a; Python and Excel MOD floor so it takes the sign of n; mathematics (Euclidean division) keeps the remainder in 0..|n|−1 no matter what. All three are shown for every run so the difference is visible, not described. The modular inverse exists only when gcd(a, n) is 1, and this tool refuses instead of guessing when it is not.