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Fermat–Catalan conjecture. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many ...
Apr 25, 2024 · Fermat’s last theorem, the statement that there are no natural numbers (1, 2, 3,…) x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2. For example, if n = 3, Fermat’s last theorem states that no natural numbers x, y, and z exist such that x3 + y 3 = z3 (i.e., the sum of two cubes is not a cube).
- The Editors of Encyclopaedia Britannica
Fermat's Last Theorem. Fermat's last theorem (also known as Fermat's conjecture, or Wiles' theorem) states that no three positive integers \ (x,y,z\) satisfy \ (x^n + y^n = z^n \) for any integer \ (n>2 \). Although a special case for \ (n=4\) was proven by Fermat himself using infinite descent, and Fermat famously wrote in the margin of one of ...
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Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The scribbled note was discovered posthumously, and the original is now lost. However, a copy was preserved in a book published by Fermat's son. In the note, Fermat claimed to have discovered a proof that the Diophantine ...
Wiles says that Fermat's Last Theorem has sparked two periods of intense progress in the past: one in the 19th century when the foundations for Wiles' areas of mathematics were laid in attempts to prove Fermat's Last Theorem, and one in the 1980s, which finally lead to the proof. The proof itself, Wiles says, has helped to ring in a new era.
Hence Fermat's Last Theorem splits into two cases. Case 1: None of x, y, z x,y,z is divisible by n n . Case 2: One and only one of x, y, z x,y,z is divisible by n n. Sophie Germain proved Case 1 of Fermat's Last Theorem for all n n less than 100 and Legendre extended her methods to all numbers less than 197.
Jun 25, 2021 · A 1670 edition of a work by the ancient mathematician Diophantus (died about 280 B.C.E.), with additions by Pierre de Fermat (d. 1665). Fermat's note on Diophantus' problem II.VIII went down in history as his “Last Theorem.” (Photo: Wikimedia Commons, Public domain)
