Meet with Mathematical Modulo

Received: 25-Jan-2021 Accepted Date: Jan 27, 2021; Published: 29-Jan-2021, DOI: 10.37532/2752-8081.21.5.18

Citation: Lenin Richardson. Ways of Euclidean Algorithmic Thinking. J Pure Applied Mathematics. 2021; 5(1):1-1.

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Modulo Arithmetic is an unusually versatile tool discovered by Gauss in 1800s. Two numbers a and b are said to be equal or congruent modulo N
iff N|(a-b), i.e. if their difference is exactly divisible by N. Usually (and on this page) a,b, are nonnegative and N a positive integer. We write a = b (mod N).
RESIDUE CLASSES:
Resultant outputs are often named as residues; accordingly, [a]'s are also know as the residue classes.Modulo Maths is a special type of arithmetic that involves only integers. This goal of this article is to explain the basics of modular arithmetic while presenting a progression of more difficult and more interesting problems that are easily solved using modular arithmetic.

EXPONENTIAL MODULO:

Exponents are just repeated multiplication, makes sense that modulo maths would make many problems involving exponentials easier. In fact, the advantage in computation is even larger and we explore it a great deal more in the intermediate modulo maths research.

MODULUS APPLICATIONS:

Modulo Maths is an extremely flexible problem solving tool and its applicable in the fields of:

Div –Divisible congruences

Line –Linearity criteria

Divisibility criteria, ways of telling whether one number divides another without actually carrying the division through. Implicit in this concept is the assumption that the criteria in question affords a simpler way than the the outright division to answer the question of divisibility.

Divisibility criteria constructed in terms of the digits that compose a given number, and,

Linearity fully filled congruences criteria, yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.