Fermat's theorem on sums of two squares
Teorema de Fermat sobre la suma de dos cuadrados
- Date
- 1640 · confidence high
- Place
- Toulouse, France
- Credited to
- Pierre de Fermat
- Field
- Knowledge & symbols
What was discovered
A number-theory theorem stating that an odd prime p can be written as a sum of two squares if and only if p is congruent to 1 modulo 4. Primes satisfying this property are called Pythagorean primes.
Stated by Fermat in 1640 in a letter to Mersenne, without proof; the first complete proof was given by Euler in 1749.
What it led to
- classification of Pythagorean primes
- later development of the theory of quadratic forms
- the first complete proofs by Euler a century later