Quasars — the brightest objects in the universe — are powered by supermassive black holes at the heart of early galaxies.

The European Space Agency's Euclid space telescope has discovered 31 of the most ancient quasars ever found. Two of these ...

N=100a+b,\quad s=a+b \,. 99\mid s(100-s) \,. Using $${100\equiv 1\pmod{99}}$$, 99\mid s(1-s) \Leftrightarrow 99\mid s(s-1) \,. Since $${99=9\cdot 11}$$ and $${\gcd(s ...

In this article we prove two characterizations of the Euclidean ball: (i) the only convex body in ℝ³ such that every normal plane bisects the volume (or surface area) is the Euclidean ball, (ii) the ...

Abstract: Coprime pairs of integer matrices have applications in various fields, including multirate systems and multidimensional signal processing. This paper addresses problems related to coprime ...

Mystical's structure is based around 'rings' with inner and outer borders - the outermost ring starts at the 3 o'clock position and flows counterclockwise, performing tasks depending on the shape it ...

Note: Some of the code here is old and was written when I was learning C++. It might be possible that code is not safe or making wrong assumptions. Please use with caution. Pull requests are always ...

Algorithms are pre-defined, self-contained sets of instructions designed to execute diverse functions, and they have been around for longer than you might expect. From ancient Babylon to the present ...