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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1] For example, the constant π may be defined as the ratio of the length of a circle's circumference to ...
Apéry's constant arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio, computed using quantum electrodynamics. [ 9 ] ζ ( 3 ) {\displaystyle \zeta (3)} is known to be an irrational number which was proven by the French mathematician Roger Apéry in 1979.
A fixed and well-defined number or other non-changing mathematical object, or the symbol denoting it. [1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. [3] A function whose value remains unchanged (i.e., a constant function). [4]
In certain cases, algorithms or other methods exist for proving that a given expression is non-zero, or of showing that the problem is undecidable.For example, if x 1, ..., x n are real numbers, then there is an algorithm [2] for deciding whether there are integers a 1, ..., a n such that
6174 is known as Kaprekar's constant [1] [2] [3] after the Indian mathematician D. R. Kaprekar.This number is renowned for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).
The definition of the Champernowne constant immediately gives rise to an infinite series representation involving a double sum, = = = (+), where () = = is the number of digits between the decimal point and the first contribution from an n-digit base-10 number; these expressions generalize to an arbitrary base b by replacing 10 and 9 with b and b − 1 respectively.
Pages in category "Unsolved problems in number theory" The following 106 pages are in this category, out of 106 total. This list may not reflect recent changes .
Landau's fourth problem asked whether there are infinitely many primes which are of the form = + for integer n. (The list of known primes of this form is A002496 .) The existence of infinitely many such primes would follow as a consequence of other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture .