Explore the fascinating world of modulo operations, especially when dealing with negative numbers. This powerful tool provides accurate remainders, crucial for cryptography, computer science, and number theory. Easily calculate 'a mod n' for any integer 'a' and modulus 'n', ensuring correct results even with negative inputs. Our calculator uses the mathematical definition where the remainder's sign matches the modulus.
Formula:
The modulo operation finds the remainder of a division of one number by another. For integers a (dividend) and n (modulus), a mod n = r, where:
- a is the Dividend (any integer)
- n is the Modulus (any non-zero integer)
- r is the Remainder (the result)
The calculation is based on the formula: a = qn + r, where q is the quotient, and r satisfies 0 ≤ r < n if n > 0, or n < r ≤ 0 if n < 0. This ensures the remainder's sign matches the modulus.