In mathematics, the Goldbach–Euler theorem (also known as Goldbach's theorem), states that the sum of 1/(p − 1) over the set of perfect powers p, excluding...

remembered today for Goldbach's conjecture and the Goldbach–Euler Theorem. He had a close friendship with famous mathematician Leonhard Euler, serving as inspiration...

Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem Goldbach's comet, a plot of the so-called Goldbach function Goldbach–Euler...

On 7 June 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture:...

In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, is the...

relating the product and series representations of the Euler function Π(1 − xn) Goldbach–Euler theorem, stating that sum of 1/(k − 1), where k ranges over...

quarto). See F. Rudio, Leonhard Euler (Basel, 1884). and Christian Goldbach, Leonhard Euler und Christian Goldbach, Briefwechsel, 1729-1764. A. P. Juskevic...

first son was Johann Albrecht Euler, whose godfather was Christian Goldbach. Three years after his wife's death in 1773, Euler married her half-sister, Salome...

function Ramanujan's master theorem Spouge's approximation Stirling's approximation Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile...

Christian Goldbach on 25 November 1731. The first appearance of e in a printed publication was in Euler's Mechanica (1736). It is unknown why Euler chose...

Fermat's Two Squares Theorem", Discrete Mathematics 339:4:1410–1411 (6 April 2016) doi:10.1016/j.disc.2015.12.002 Euler à Goldbach, lettre CXXV De numeris...

{1}{26}}+{\frac {1}{31}}}+\cdots =1.} This is sometimes known as the Goldbach–Euler theorem. Detecting whether or not a given natural number n is a perfect...

prime. Christian Goldbach formulated Goldbach's conjecture, that every even number is the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's...

number theorem § Prime number race.) In 1923, Hardy and Littlewood showed that the generalized Riemann hypothesis implies a weak form of the Goldbach conjecture...

Examples of this are Fermat's Last Theorem, which was proved 358 years after the original formulation, and Goldbach's conjecture, which remains unsolved...

noted by J. A. Euler, the son of Leonhard Euler, in about 1772. The Ideal Waring Theorem would be an unconditional strengthening of Euler's observation:...

is now known as one of the two Sophomore's dream identities. The Goldbach–Euler theorem states that the sum of the reciprocals of the numbers that are 1...

well-known theorems have even more idiosyncratic names, for example, the division algorithm, Euler's formula, and the Banach–Tarski paradox. A theorem and its...

postulate is also called the Bertrand–Chebyshev theorem or Chebyshev's theorem. Chebyshev's theorem can also be stated as a relationship with π ( x )...

correct solution. Goldbach's conjecture The twin prime conjecture The Collatz conjecture The Manin conjecture The Maldacena conjecture The Euler conjecture,...

in 1859. The prime number theorem was finally proved by Jacques Hadamard and Charles de la Vallée-Poussin in 1896. Goldbach and Riemann's conjectures...

a_{4}b_{1}\right)^{2}.\end{aligned}}} Euler wrote about this identity in a letter dated May 4, 1748 to Goldbach (but he used a different sign convention...

multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal...

about the original function. Euler showed that the fundamental theorem of arithmetic implies (at least formally) the Euler product ∑ n = 1 ∞ 1 n s = ∏...

1640 and 1657. Euler sent a letter to Goldbach on 4 August 1753 in which claimed to have a proof of the case in which n = 3. Euler had a complete and...

identified by L. Euler in a letter to Goldbach written on 4 May 1748," and they comment that "it makes no sense whatsoever to say that Euler "identified"...

induction. From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common integer factor...

is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics...

(2013). "Major arcs for Goldbach's theorem". arXiv:1305.2897 [math.NT]. Helfgott, Harald A. (2012). "Minor arcs for Goldbach's problem". arXiv:1205.5252...

on prime numbers]. Comptes rendus (in French). 29: 397–401. L. Euler, Letter to Goldbach. 16-12-1752. Pintz, János (2006-07-01). "A note on Romanov's constant"...