On the Diophantine Equation $$dx^2+p^{2a}q^{2b}=4y^p$$

Abstract

We study the exponential Diophantine equation x 2 +p m q n = 2y p in positive integers x, y, m, n, and odd primes p and q using primitive divisors of Lehmer sequences in combination with elementary number theory. We discuss the solvability of this equation.

Advances in Slime Mould Algorithm: A comprehensive Survey

“…Moreover the researchers hybridize SMA with sine cosine algorithm(SCA) [81] , particle swarm optimization (PSO) [104], evolutionary algorithm(EA) [106], firefly algorithm(FA) [106],grey wolf optimization algorithm(GWOA) [107], marine predators algorithm(MPA) [108], gradient-based optimizer(GO) [109], quadratic approximation(QA) [110], tournament selection(TS) [111], artificial neural network(ANN) [112]],Moth-flame optimization algorithm(MFOA) [113], pattern search algorithm(PSA) [114], support vector regression(SVR) [115] and etc. These hybrid SMA variants have indicated their merits such as the well balance between exploration and exploitation, good convergence speed, avoiding premature convergence, less computation time and so on.…”

“…Wenhe He et al [64] proposed an unresolved peaks analysis algorithm, which was based on the sigmoidal membership function, Lévy flight, and slime mould algorithm (SLSMA), for microchip electrophoresis (ME) signal detection. Chakraborty P et al [110]proposed a hybrid SMA for three engineering optimization problems. From the evaluations, HSMA was an efficient algorithm for reallife problems.…”