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...

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...

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

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

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...

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

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...

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...

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...

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

a French École Normale Supérieure as she attempts to prove the Goldbach–Euler theorem together with her fellow student Lucas (Julien Frison, a graduate...

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...

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...

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...

{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...

Fermat polygonal number theorem, that every positive integer is a sum of at most n of the n-gonal numbers Waring–Goldbach problem, the problem of representing...

The interest of Leonhard Euler (1707–1783) in number theory was first spurred in 1729, when a friend of his, the amateur Goldbach, pointed him towards some...

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...

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"...

inaccurately) that it could be found in a letter from Leonhard Euler to Christian Goldbach. The identity can be proven simply by multiplying the two terms...

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

theorem Method of successive substitution Chinese remainder theorem Fermat's little theorem Proofs of Fermat's little theorem Fermat quotient Euler's...

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...

persist: theorems often enough may still be referred to as conjectures, using the anachronistic names. Deligne's conjecture on 1-motives Goldbach's weak conjecture...

series; what if there were another? In a 1745 letter to Christian Goldbach, Euler claimed that he was not aware of any such counterexample, and in any...

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

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