A unified approach in manipulation with modular arithmetic

Modular arithmetic lets us carry out algebraic calculations on integers with a systematic disregard for terms divisible by a certain number (called the modulus). This kind of reduced algebra is essential background for the mathematics of computer science, coding theory, primality testing, and much more. In this paper we propose a unique approach for calculating “mod” operation, regardless of the signs of operands by which all ambiguities present in high level languages, such as C, Java, C++, Mathematica, Matlab, are overcome. Modular arithmetic is quite a useful tool in number theory. In particular, it can be used to obtain information about the solutions (or lack thereof) of a specific equation. In order to reduce the number of iteration steps during the calculation of g.c.d. and solving linear diophantine equations in two variables, based on Euclidian and extended Euclidian algorithm, we propose the usage of mod and mod operations.