A series of papers in elementary number theory, generalizing some known well-known results and showing other unexplored regions. Generalized Arithmetic Progressions - A Survey Generalized Geometric Progressions - A Survey The Multinomial Theorems Triangular Numbers - Some General Theorems and Related Results In nite Sequential Averages A Generalized Elementary Sequence and Its Sum Rectangles, Golden Rectangle - A Brief Note Matrix Properties of the Most Generalized Fibonacci Sequences In nite Family of Generalized Fibonacci Polynomials A General In nite Family of Congruence Relations In nite Families of Base Systems and Properties of Numbers Some General Properties of Arithmetic Functions and a Few Conjectures Some General Divisibility Statements Some General Results in Elementary Number Theory A Remarkable Consequence of the Dirichilet's Theorem Some Fundamental Conjectures on the Distribution of Prime Numbers"