Modular arithmetic and quadratic reciprocity
Aritmética modular y reciprocidad cuadrática (Disquisitiones Arithmeticae)
- Date
- 1801 · confidence high
- Place
- Brunswick and Göttingen, Germany
- Credited to
- Carl Friedrich Gauss
- People
- 👤 Carl Friedrich Gauss1777–1855
- Field
- Knowledge & symbols
What was discovered
The introduction of congruence notation and a systematic treatment of remainders, quadratic forms and roots of unity, with the first proof of the law of quadratic reciprocity and the construction of the 17-sided polygon. It founds modern number theory.
Gauss gave eight different proofs of quadratic reciprocity over the course of his life.
What it led to
- algebraic number theory
- public-key cryptography
- ring theory
- Artin and Langlands reciprocity
Built on
- Fermat Last Theorem statement and infinite descentc. 1637
- Euler
- Legendre (statement of reciprocity)