| The theory of continued fractions has applications in cryptographic problems and in solution methods for Diophantine equations. We will first examine the basic properties of continued fractions such as convergents and approximations to real numbers. Then we will discuss a computationally efficient attack on the RSA cryptosystem (Wiener's attack) based on continued fractions. Finally, using continued fractions and solutions of Pell's equation, we will show that the Diophantine equation x4-kx2y2+y4=2 j&parl0; j,k∈N&parr0; has no nontrivial solutions for j = 9, 10, 11 given that k > 2 and k is not a perfect square. |
