Euclidean Division and Simple Elements

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Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Explains the conversion between decimal and fractional writing, including division with remainder and a trick for periodic numbers.

Covers rational numbers, amplifying and simplifying fractions, and calculating values.

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Covers the extension of addition and multiplication operations in rational numbers.

Covers the factorization of polynomials over a field, including division with remainder and common divisors.