English

Abstract

What is the ANZL Algorithm? It is a genuine result of our work which is theoretically and practically proved. By using the ANZL Algorithm, we can test whether a given number belongs to Lucas’s series. It can also be used to find a sequence of Lucas’s numbers, starting from any number If a given number completes the relation we can say that it is a Lucas number and we mark it as From the pair of numbers we can find the preceding and the succeeding e Based on these three elements of Lucas’s series, we can create the key for data encryption and decryption. I ALGORITHM ANZL In mathematics, the numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. For centuries, mathematicians both amateurs and professionals have been intrigued by the sequence of numbers and the closely related irrational number called the golden mean. The sequence begins with: where, as you can see, each number beginning with 2 is the sum of the two immediately preceding numbers. As you progress along the list of quotients of consecutive numbers, such as: you get closer and closer to the golden mean, which is exactly: and approximately Another series quite similar to the series that often occurs when working with the series. Edouard Lucas (1842-1891) (who gave the name Fibonacci Numbers to the series written about by Leonardo of Pisa) studied this second series of numbers: called the Lucas numbers in his honour. On this page we examine some of the interesting properties of the Lucas numbers themselves as well as looking at its close relationship with the numbers. Based on Fibonacci’s series: We will be able to get the elements of Lucas’s series using: Where ! # $ and % ! & . If , is even, we use if is odd, the we use '. For and ! we have: ( ' ' For and ! we have: ) ' ( For and ! we have: