Welcome to my collection of mathematical articles. Here I publish notes, proofs, and expository pieces on topics that interest me, particularly in analysis, differential equations, algebra, and theoritical computer science. New articles will be added as I continue my studies and attempt my hand at solving the unsolved.
This article presents the following proofs:
1. On the Solution Space of an n-th Order Linear Homogeneous Differential Equation
A proof showing that the solution space of an n-th order linear homogeneous differential equation is an n-dimensional vector space: https://deepwrites.com/dimension-of-solution-space.html
2. Characterization and Analysis of a Problem from the Open Problem Garden with Connections to Finite Group Theory
A note on higher power residues modulo primes, including the case p=2, together with connections to finite group theory: https://deepwrites.com/Characterization-of-primes.html
