number theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. The conjecture states that the equation...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844...

{1}{z}}<1} . Beal's conjecture can be restated as "All Fermat–Catalan conjecture solutions will use 2 as an exponent". The abc conjecture would imply that...

Theorem for n ≥ 6 {\displaystyle n\geq 6} . The Fermat–Catalan conjecture, a generalization of Fermat's Last Theorem concerning powers that are sums of powers...

Catalan pseudoprime Catalan's triangle Catalan–Dickson conjecture Catalan–Mersenne number conjecture Catalan beta function Fermat–Catalan conjecture Fuss–Catalan...

including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem. The conjecture states that: given ε > 0, there exists...

de Fermat, a French amateur mathematician. Fermat–Apollonius circle Fermat–Catalan conjecture Fermat cubic Fermat curve Fermat–Euler theorem Fermat number...

the Goldbach conjecture". In the movie, this number is known as a "Martian prime". Cunningham chain Double exponential function Fermat number Perfect...

Fermat conjectured that all numbers of the form 2 2 m + 1 {\displaystyle 2^{2^{m}}+1} (known as Fermat numbers) were prime. However, this conjecture was...

Ramanujan–Nagell equation, 2n − 7 = x2 the equation of the Fermat–Catalan conjecture and Beal's conjecture, am + bn = ck with inequality restrictions on the exponents...

powers conjecture (disproved) concerns situations in which the sum of n integers, each a kth power of an integer, equals another kth power. The Fermat-Catalan...

(Solomon W. Golomb, 1963) Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured that all Fermat numbers are prime. Indeed...

/ n = 1 / x + 1 / y + 1 / z {\displaystyle 4/n=1/x+1/y+1/z} . Fermat–Catalan conjecture: there are finitely many distinct solutions ( a m , b n , c k...

The equations are generalisations of those considered in Fermat's Last Theorem. The conjecture is that if the sum of some k-th powers equals the sum of...

equation appears in various contexts in elementary geometry. The Fermat–Catalan conjecture concerns a certain Diophantine equation, equating the sum of two...

z} are required to be positive integers. The equation of the Fermat–Catalan conjecture: a m + b n = c k , {\displaystyle a^{m}+b^{n}=c^{k},} in which...

in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem. After moving to the CUNY Graduate...

{\displaystyle k} a nonnegative integer. They are named after Pierre de Fermat, who conjectured that all such numbers are prime. The first five of these numbers...

had referred to them in 1948 as numbers with the "Fermat property", or "F numbers" for short. Fermat's little theorem states that if p {\displaystyle p}...

Mordell curve Fermat's Last Theorem Mordell conjecture Euler's sum of powers conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle...

example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form...

problem). Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle...

integers 2 ≤ n ≤ 3 000 000 {\displaystyle 2\leq n\leq 3\,000\,000} . His conjecture was completely proved by Chebyshev (1821–1894) in 1852 and so the postulate...

of the ABC Conjecture using integer k'th roots" (PDF), New Zealand J. Math., 35 (2): 121–136 Ribenboim, P. (1979). 13 Lectures on Fermat's Last Theorem...

proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's Last Theorem. 1984 –...

part of the Taniyama–Shimura conjecture and thereby proves Fermat's Last Theorem. 1999 — the full Taniyama–Shimura conjecture is proved. 2002 — Manindra...

problem in mathematics: Are any Fortunate numbers composite? (Fortune's conjecture) (more unsolved problems in mathematics) A Fortunate number, named after...

(sequence A222119 in the OEIS) Repunit Fermat number Power of two Erdős–Borwein constant Mersenne conjectures Mersenne twister Double Mersenne number...

and 8191 (111 in base-90, 1111111111111 in base-2). The Goormaghtigh conjecture says there are only these two cases. Using the pigeon-hole principle it...