Carryless Arithmetic Mod 10

TL;DR

This paper explores a novel form of arithmetic called carryless mod 10, where carry digits are ignored, leading to a different set of arithmetic properties and prime definitions.

Contribution

It introduces the concept of carryless arithmetic mod 10 and analyzes its properties, including the altered behavior of primes and basic operations.

Findings

Prime numbers are redefined under carryless arithmetic.

Basic operations like addition and multiplication behave differently without carries.

The structure of this arithmetic system has unique algebraic properties.

Abstract

We investigate what arithmetic would look like if carry digits into other digit position were ignored, so that 9 + 4 = 3, 5 + 5 = 0, 9 X 4 = 6, 5 X 4 = 0, and so on. For example, the primes are now 21, 23, 25, 27, 29, 41, 43, 45, 47, ... .