Existence and Number of Solutions of Diophantine Quadratic Equations with Two Unknowns in ZZ and NN

In this short note we study the existence and number of solutions in the set of integers ($Z$) and in the set of natural numbers ($N$) of Diopahntine Equations of second degree with two variables of the general form $ax^2-by^2=c$.Comment: 2 page

Olivier Chesneau's work on massive stars

Olivier Chesneau challenged several fields of observational stellar astrophysics with bright ideas and an impressive amount of work to make them real in the span of his career, from his first paper on P Cygni in 2000, up to his last one on V838 Mon in 2014. He was using all the so-called high-angular resolution techniques since it helped his science to be made, namely study in details the inner structure of the environments around stars, be it small mass (AGBs), more massive (supergiant stars), or explosives (Novae). I will focus here on his work on massive stars.Comment: The Physics of Evolved Stars, Jun 2015, Nice, Franc