Math | Analytical Math | Analytical No. Theory | Gauss Lemma on Legendre l | Lect.-33 | Dr.S.S.Bel

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Congruences,
Basic properties of congruences,
Binary and decimal representation of integers,
Linear congruences and Chinese Remainder theorem,
Pierre de Fermat theorem,
Fermat’s little theorem and pseudo-primes,
Wilson’s theorem.
The order of an integer modulo n,
Primitive roots for primes,
Lagrange’s theorem,
Composite numbers having primitive roots,
The theory of indices.
Euler’s criterion,
The Legendre symbol and its properties,
Gauss Lemma,
Quadratic reciprocity,
Quadratic reciprocity law,
Quadratic congruence’s with composite moduli,
The equation x2+y2=z2,
Pythagorean triple.

The Mobius function 𝜇(𝑛),
The Eular Totient function 𝜑(𝑛),
A relation connecting 𝜇 and 𝜑,
The product formula for 𝜑(𝑛),
Dirichlet product of arithmetic function,
Dirichlet inverses and Mobius inversion formula,
The Managoldt function 𝛬(𝑛),
Multiplicative function,
Multiplicative function and Dirichlet Multiplication,
Inverse of Completely multiplicative function,
Liouville’s function,
The divisor function,
Generalized convolution,
Formal power series,
The Bell series of an arithmetic function,
Bell series
Dirichlet multiplication,
Derivatives of arithmetic function,
The Selberg identity.