New Methods Based on the Calculation of Specific Decimal Fractions for Decomposing an Integer into a Product of Prime Factors

Abstract

Bouchab Bahbouhi

This article presents for the first time two methods for decomposing integers in products of prime factors which are based on the calculation of decimal fractions. Its originality lies in the fact that the divisors used are decimals and not prime divisors and in addition the decimal part is manipulated in such a way that two decimal digits are fixed and the others are variable. In the first method, the divisors are of type 2n and which have a very interesting particularity which is that they always have two same digits at the end of their decimal parts (25 or 75). And it is this particularity which is exploited to develop these methods. The other method introduces a new notion that of the decomposition key which is a product of prime factors used to decompose all numbers having the same number of digits. It is similar to the first method because it also uses decimal fractions for the calculation and the denominator is the square root. This article paves the way for new applications in computer science.

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