Fermat's Theorem on Sums of Two Squares states that an odd prime number can be written as the sum of two perfect squares if and only if it leaves a remainder of one when divided by four. Attributed to Pierre de Fermat, it is a classical result of number theory that was later given a full proof by Leonhard Euler.
Facts
StatementThe theorem states that an odd prime p can be written as the sum of two integer squares if and only if p leaves remainder 1 when divided by 4. 1 Proof YearFermat stated the claim without a published proof in a December 25, 1640 letter to Marin Mersenne. Euler gave the first proof, by infinite descent, communicated in an April 12, 1749 letter to Goldbach. Classification
Statement Form Statement FormCharacterization Theorem 1 Connections
In Branch
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Posed By
Proved By
Sources
1. Fermat's Theorem on Sums of Two Squares (Wikipedia)
Wikimedia FoundationWikipedia, Fermat's theorem on sums of two squares, lead section
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as:
Wikipedia, Fermat's theorem on sums of two squares, Euler's proof section
Euler succeeded in proving Fermat's theorem on sums of two squares in 1749, when he was forty-two years old. He communicated this in a letter to Goldbach dated 12 April 1749.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.