In these “Number TheoryNotes PDF”, you will study the micro aptitude of understanding aesthetic aspect of mathematical instructions and gear young minds to ponder upon such problems. Also, another objective is to make the students familiar with simple number theoretic techniques, to be used in data security.
The topics we will cover will be taken from the following list:
Distribution of Primes and Theory of Congruencies: Linear Diophantine equation, Prime counting function, Prime number theorem, Goldbach conjecture, Fermat and Mersenne primes, Congruence relation and its properties, Linear congruence and Chinese remainder theorem, Fermat’s little theorem, Wilson’s theorem.
Number Theoretic Functions: Number theoretic functions for sum and number of divisors, Multiplicative function, Möbius inversion formula, Greatest integer function. Euler’s phi-function and properties, Euler’s theorem.
Primitive Roots: The order of an integer modulo n, Primitive roots for primes, Composite numbers having primitive roots; Definition of quadratic residue of an odd prime, and Euler’s criterion.
Quadratic Reciprocity Law and Public Key Encryption: The Legendre symbol and its properties, Quadratic reciprocity, Quadratic congruencies with composite moduli; Public key encryption, RSA encryption and decryption.
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