Fundamental theorem of arithmetic
Teorema fundamental de la aritmética
- Date
- c. 300 BCE-1801 · confidence medium
- Place
- Brunswick, Germany
- Credited to
- Carl Friedrich Gauss (first rigorous proof of uniqueness); preceded by Euclid
- Field
- Knowledge & symbols
What was discovered
Every integer greater than one factors uniquely into primes. Euclid already used the key result (his lemma), but Gauss gives a fully rigorous proof in 'Disquisitiones Arithmeticae'.
Euclid proved the restricted case (exponents equal to one); the Persian mathematician al-Farisi gave a more complete statement in the 13th century before Gauss's general proof.
What it led to
- Modern number theory
- Gauss's law of quadratic reciprocity
- Generalisation to rings and unique factorisation domains