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The problem to determine all positive integers such that the concatenation of and in base uses at most distinct characters for and fixed [citation needed] and many other problems in the coding theory are also the unsolved problems in mathematics.
Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers. Determining whether a given initial point with rational coordinates is periodic, or whether it lies in the basin of attraction of a given open set, in a piecewise-linear iterated map in two dimensions ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
The real part of every nontrivial zero of the Riemann zeta function is 1/2. The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of 1 / 2 . A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime ...
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the program, whether ...
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