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The original conjecture spawned as Erdős and Turán sought a partial answer to Sidon's problem (see: Sidon sequence). Later, Erdős set out to answer the following question posed by Sidon: how close to the lower bound | B ∩ [ 1 , n ] | ≥ n 1 / h {\displaystyle |B\cap [1,n]|\geq n^{1/h}} can an additive basis B {\displaystyle B} of order h ...
This is related to the Erdős multiplication table problem. [4] The best lower bound on | A · A | for this set is due to Kevin Ford. [5] This example is an instance of the Few Sums, Many Products [6] version of the sum-product problem of György Elekes and Imre Z. Ruzsa.
The conjecture is named after Paul Erdős and Ernst G. Straus, who formulated it in 1948, but it is connected to much more ancient mathematics; sums of unit fractions, like the one in this problem, are known as Egyptian fractions, because of their use in ancient Egyptian mathematics.
An entity–relationship model (or ER model) describes interrelated things of interest in a specific domain of knowledge. A basic ER model is composed of entity types (which classify the things of interest) and specifies relationships that can exist between entities (instances of those entity types).
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The Erdős Distance Problem consists of twelve chapters and three appendices. [5]After an introductory chapter describing the formulation of the problem by Paul Erdős and Erdős's proof that the number of distances is always at least proportional to , the next six chapters cover the two-dimensional version of the problem.
One can interpret the positions of the numbers in a sequence as x-coordinates of points in the Euclidean plane, and the numbers themselves as y-coordinates; conversely, for any point set in the plane, the y-coordinates of the points, ordered by their x-coordinates, forms a sequence of numbers (unless two of the points have equal x-coordinates).
(more unsolved problems in mathematics) Erdős' conjecture on arithmetic progressions can be viewed as a stronger version of Szemerédi's theorem. Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture.