Number Theory

This topic covers concepts such as Squares and Square Roots, Co-prime Numbers, Real Numbers, Irrational Numbers, Rational Numbers, Triangular Numbers, Perfect Cube, Perfect Numbers, Prime and Composite Numbers, and Cyclicity.

This topic covers concepts such as Laws of Surds, Simplification of Surds, Rules and Properties of Surds, Power Rule of Surds, Multiplication Rule of Surds, Multiplication Rule of Surds with Equal Base, Division Rule of Surds, Compound Surds, etc.

This topic covers concepts such as Rules of Divisibility, Euclid’s Division Lemma, Euclid Division Algorithm, Tests for Divisibility, Rule for Divisibility by 10, Rule for Divisibility by 5, Rule for Divisibility by 2, etc.

This topic covers concepts such as HCF and LCM of Fractions, Highest Common Factor (HCF), HCF of Two Positive Integers using Euclid’s Division Algorithm, Lowest Common Multiple, and Properties of GCD.

This topic covers concepts such as Prime Numbers, Prime Factorization, Test for a Number to be Prime, Twin Primes, Fundamental Theorem of Arithmetic, Euclidean Theorem, and Sophie Germain Identity.

This topic covers concepts such as Graph of Greatest Integer Function [x], Properties of Greatest Integer Function [x], Greatest Integer Function [x], Special Inequality Based on Greatest Integer Function [x], Fractional Part Function {x}, etc.

This topic covers concepts such as Addition and Multiplication Operations in Modulo System, Congruence Modulo, Modulo Operation, and Properties of Congruence.

This topic covers concepts such as Complete Residue Modulo, Euler’s Totient Function, Fermat's Little Theorem, Euler's Theorem, Carmichael's Theorem, Wilson's Theorem, Chinese Remainder Theorem, Digit Sum Characteristic Theorem, etc.