Mathematics · Avançado · Nível 3

Number theory

Divisibility and the division algorithm, Euclid's algorithm and Bézout's identity, unique factorisation and the divisor functions; congruences, inverses, linear congruences and the Chinese remainder theorem, with the divisibility tests they explain; Fermat's little theorem, Euler's totient and theorem, Wilson's theorem, and the arithmetic public-key cryptography rests on; orders and primitive roots, quadratic residues, the Legendre symbol, Euler's criterion and quadratic reciprocity; linear Diophantine equations, Pythagorean triples, sums of two squares, continued fractions and Pell's equation; and the distribution of primes, from Euclid's proof and the sieve to the prime number theorem and Dirichlet's theorem on arithmetic progressions.

Ages 18+ 26 lessons about 11 hours in all

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