AN APPRAISAL ALGORITHM FOR TESTS OF DIVISIBILITY USING MODULAR ARITHMETIC

Abstract

Knowledge to execute wild conceptual mathematical computations helped immensely even out of the park. Knowing these quick calculations has been of great interest ever since. Divisibility tests were required to know whether a number (large enough) was divisible by a given integer or not? Let 0,m  and a be any integer. The symbol, mod , am was used to represent the residue when a was divided by m. In this piece of treatised work, modulo residue theory was employed to find tests of divisibilty for even numbers < 60 and elaborated the use of modular arithmetic from number theory in finding different tests of divisibility. Particularly, b adic expension of an integer N and its congruence modulo b was used to characterise a given integer regarding its divisibility rule. One of the characterisations was stated and proved that an integer N was divisible by 40 if and only if
0 1 2 10( 2 ) a a a was divisible by 40, where 0 1 2 ,, a a a
were the digits of N in its decimal representation. Finally, the framework proposed reduced the pitfalls by demonstating each established rule with the help of their recursive applications on large integers.