Authors: Marius Coman
In this book I define a function which allows the reduction to any non-null positive integer to one of the digits 1, 2, 3, 4, 5, 6, 7, 8 or 9. The utility of this enterprise is well-known in arithmetic; the function defined here differs apparently insignificant but perhaps essentially from the function modulo 9 in that is not defined on 0, also can’t have the value 0; essentially, the mar reduced form of a non-null positive integer is the digital root of this number but with the important distinction that is defined as a function such it can be easily used in various applications (divizibility problems, Diophantine equations), a function defined only on the operations of addition and multiplication not on the operations of subtraction and division. Some of the results obtained with this tool are a proof of Fermat’s last Theorem, cases n = 3 and n = 4, using just integers, no complex numbers and a Diophantine analysis of perfect numbers. Note: I understand, in this book, the numbers denoted by “abc” as the numbers where a, b, c are digits, and the numbers denoted by “a*b*c” as the products of the numbers a, b, c.
Comments: 62 Pages.
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