
Explore the divisibility theorem and its core properties, with proofs and practical problem-solving methods, including testing divisibility and solving largest-n cases like n^3+100 divisible by n+10.
Explore divisibility tests for numbers like 2, 3, 5, 6, 7, 8, 9, 10, and 11, learn proofs and applications via Euclid's division lemma and test methods.
Explore the greatest common divisor and least common multiple, their Euclid's division lemma foundations, and Bézout's identity, with key properties for integers and coprime cases.
Explore the definition and core properties of prime numbers, including divisibility and prime factorization, and apply Bertrand's postulate and Euclid's theorem to solve problems in number theory.
Explore modular arithmetic and congruence modulo m, learn core properties, and apply them to solve problems from quadratic residues to last-digit patterns and decimal representations.
Explore modular arithmetic with prime factorization, tau and sigma functions, and Euler’s totient to compute remainders and inverses, apply Fermat’s and Euler’s theorems, and use Wilson’s theorem in problem solving.
defines perfect squares, gives examples, and explains how to recognize them using digit endings and modular properties (0 or 1 mod 2, 3, 4, 8); demonstrates problem-solving strategies with square-related questions.
Explore the greatest integer function and fractional part, its properties, and Hermite's identity through definitions, proofs, and solved problems to sharpen number theory skills.
If You have understood Basics of Mathematics Course then Number Theory Course will go smooth.
Number Theory is useful in a lot of competitive Exams. Even though it may not be directly listed in Syllabus, its concept appear as sub-parts of Problems.
Number theory sometimes looks obvious and sometimes very difficult to observe. In this course I have moved from Concepts to Concepts covering supporting problems and techniques to handle certain situations. Number Theory certainly uses some algebraic techniques as well as useful theorems to deduce more conclusions.
This Course include some very useful sections of Number theory and are very beginner level concepts. Yet the variety of problems this course aim to solve is huge. These sections of Number theory are quite useful for competitive Exams. I have made sure that my approach is problem solving and not jargon.
There could be few lectures that you might need to watch more than once to grasp it completely. This course will build problem solving skills in you and will set you up to solve even Higher level exams like International Math Olympiads.
This course has video lectures, notes in pdf and workbooks to help you test your understanding along the way. To Navigate it better, Basics of Mathematics is organised into the following Sections
1) Divisibility Theorem
2) Greatest Common Divisor and its properties
3) Primes and its properties
4) Understanding of Modular Arithmetic
5) Theorems in Modular Arithmetic
6) Perfect Squares and Perfect cubes
7) Greatest Integer functions and its properties
Each Subsection will have a set of video lectures followed by Assignments based on what is being taught in the section. Attempting
Assignment before moving to another section will be beneficial. Any doubts regarding the course can be asked in Q&A.
I hope you enjoy the course,
All the best