The three pillars of machine programming

In this position paper, we describe our vision of the future of machine programming through a categorical examination of three pillars of research. Those pillars are: (i) intention, (ii) invention, and (iii) adaptation. Intention emphasizes advancements in the human-to-computer and computer-to-machine-learning interfaces. Invention emphasizes the creation or refinement of algorithms or core hardware and software building blocks through machine learning (ML). Adaptation emphasizes advances in the use of ML-based constructs to autonomously evolve software

On some Diophantine equations

for p >= 3 and a square-free integer p(2) - 4. In addition to these, all solutions of some different Diophantine equations such as x(2) - v(2n)xy + y(2) = -(p(2) - 4)u(n)(2), x(2) - v(n)xy + y(2) = -(p(2) - 4), x(2) - v(n)xy + y(2) = 1, x(2) - v(2n)xy + y(2) = u(n)(2), x(2) - v(2n)xy + y(2) = v(n)(2), x(2) - (p(2) - 4)u(n)xy - (p(2) - 4)y(2) = 1 are identified, by using divisibility rules of the sequences (u(n)) and (v(n))