The sequence, whose initial condition is 2 and 1, obtained by summing the two terms preceding it, is called the Lucas sequence. The terms of this series continue as 2, 1, 3, 4, 7, 11, 18, 29, ... respectively. The features of the Lucas sequence have been studied in many projects in the literature and many studies have been done on Lucas series in applied sciences. Cryptology is the science that deals with encrypting data, transferring it securely from one point to another, and converting the encrypted data to the previous one. It includes cryptography and cryptoanalysis. Different encryption-decryption methods have been developed to ensure the security of the data from the past to the present. Some of these are Caesar, Affine, Vigenere and RSA. There are two types of encryption systems in cryptology. The first one is symmetric (secret key) encryption and the another one is asymmetric (public key) encryption. In this study; using the features of the Lucas sequence, studies on cryptology, which deals with the correct encryption, transfer and decryption of data, have been carried out and an example of cryptology algorithm has been given. With Lucas cipher, the letters in the alphabet and the space character are each mapped to the terms of the Lucas sequence. Later, starting from the first term of the Lucas sequence, the encryption was strengthened by adding Lucas terms. As a result, the text to be encrypted has been turned into a symbolic representation of the numbers. Then, the necessary information for deciphering the text which is encrypted with numbers is given.
Abstract:The designs which are made with FSS (frequency selective surfaces) analysis can be in different shapes and sizes. Square, round, plus, triangle, snowflake etc. are some of them. In this article, BSF (band stop filter) is designed by using FSS with the Golden Ratio Rule which is found by Fibonacci. In Golden Ratio Rule, each number is the sum of two numbers coming before that number and the ratio of every sequential number equals approximately 1.618, exact 1.618 at last. In design, Golden Ratio Rule is used while forming thickness, width and length. All of the simulations are run in CST (computer simulation technology) computer program between 700 MHz and 1,700 MHz in frequency domain section. There is not any active or passive component in the design. Only 80 cm × 130 cm copper plate and the shapes over it, the BSF with 1.35 GHz CF (center frequency) and 41 MHz BW (bandwidth) frequency is formed and has become ready to perform. If shapes and sizes are changed while preserving the ratio, it can be reachable different CF and BW frequencies. After obtaining the OF, the design will block the electromagnetic effects in accordance with BSF, and electric or magnetic waves cannot transmit from the copper plate, as a result; harmful side effects can be stopped.
Let k 3 be an odd integer. In this paper we investigate all positive integer solutions of the equations x 4 kx 2 y C y 2 D A, x 4 kx 2 y C y 2 D A.k 2 4/; x 4 .k 2 4/y 2 D 4A; and x 2 .k 2 4/y 4 D 4A with A D .k 2/: We show that if k Á 1.mod 8/ and k 2 4 be a square-free integer; then the equation x 4 kx 2 y C y 2 D .k 2/.k 2 4/ has no positive integer solutions. Moreover, if k 2 4 be a square-free integer; then the equation x 4 kx 2 y C y 2 D .k C 2/.k 2 4/ has no positive integer solutions.
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