The paper proposes a new method, called the Fast Quadratic Transform (FQT), to solve the general indefinite two-variable quadratic equation in integers. The paper presents the new approach, discusses its properties, and provides a comparative evaluation with the classical technique. The FQT is demonstrated to be markedly superior for all cases in which it applies, including examples for more th...

Let E be an elliptic curve over Q without complex multiplication, and for each prime p of good reduction, let nE(p) = |E(Fp)|. For any integer b, we are studying in this paper elliptic pseudoprimes to the base b. More precisely, let QE,b(x) be the number of primes p 6 x such that bE ≡ b (modnE(p)), and π E,b (x) be the number of compositive nE(p) such that b nE(p) ≡ b (modnE(p)) (also called el...

In this paper, a finite-horizon optimal control problem involving dynamical system described by linear Caputo fractional differential equation and quadratic cost functional is considered. An explicit formula for the value given, which includes solution of certain Fredholm integral equation. A step-by-step feedback procedure constructing $ \varepsilon $-optimal controls with any accuracy > 0 ...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.