This ebook with over 200 pages covers all major concepts in Number Theory and Inequalities. Well explained concepts, tons of examples with detailed explanations, easy to remember formulae, challenging questions and good shortcuts / tips wherever applicable are included in the ebook.

The following concepts in Number Theory are covered in the eBook.

1. Definition of types of numbers from Natural Number to Real numbers, complex numbers and their conjugates.
2. Irrational numbers, surds, binomial quadratic surds and their conjugates.
3. Method to determine if a given number is a prime number.
4. Concepts and examples of co-prime numbers.
5. Tests of divisibility including shortcuts for divisibility of numbers such as '7' and '13'.
6. Concepts and word problem examples to elucidate LCM and HCF.
7. Fractions - Proper fractions, improper fractions, LCM and HCF of fractions.
8. Factors and method to find the number of factors for a given integer. Method to find the sum of all positive factors of a natural number.
9. Properties of remainders and quotients of division of large numbers such as 2³⁷¹.
10. Remainder theorem and its application with examples, which is considered to be a difficult topic with tough questions is explained with examples.
11. Factorials and highest power of a number contained in a factorial.
12. Properties of unit digits of numbers raised to large powers. For example unit digit of 3231¹⁷⁹.
13. Conversion of numbers from one base to another and back to decimal notation.
14. 19 illustrative examples to explain the concepts; 34 solved examples (with shortcuts wherever applicable) to acquaint you with as many different questions as possible; 27 exercise problems with answer key and explanatory answers to provide you with practice.

The following concepts in Inequalities are covered in the eBook.

1. Explanation to the basic concept of inequalities
2. Various basic rules governing inequalities such as multiplying both sides of an inequality with a negative number, inequalities with algebraic equations such as quadratic expressions, inequalities with exponents, inequalities with modulus
3. 16 solved examples, with additional notes wherever needed to help solve questions in inequalities quickly.
4. 17 exercise problems with the answer key and explanatory answers

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