Explore fundamental concepts in number theory through a 30-minute lecture covering perfect numbers, Mersenne primes, abundant numbers, and deficient numbers. Delve into Wilson's Theorem, the Euclidean Algorithm, Fermat's Little Theorem, and Diophantine equations. Gain insights into the Prime Number Theorem and learn about polynomials with one unknown in the context of Diophantine equations. Enhance your understanding of these essential mathematical principles and their applications in number theory.