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Cross-figure. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells. Clues may be mathematical ("the seventh prime number"), use general knowledge ("date of the ...
The prime number theorem for arithmetic progressions deals with the asymptotic distribution of prime numbers in an arithmetic progression. Covering by and partitioning into arithmetic progressions. Find minimal l n such that any set of n residues modulo p can be covered by an arithmetic progression of the length l n.
Kakuro or Kakkuro or Kakoro (Japanese: カックロ) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword. Kakuro puzzles are regular features in many math-and-logic puzzle publications across the world. In 1966, [1] Canadian Jacob E. Funk, an employee of Dell Magazines, came up with the ...
Then P(n) is true for all natural numbers n. For example, we can prove by induction that all positive integers of the form 2n − 1 are odd. Let P(n) represent " 2n − 1 is odd": (i) For n = 1, 2n − 1 = 2 (1) − 1 = 1, and 1 is odd, since it leaves a remainder of 1 when divided by 2. Thus P(1) is true.
Analytic number theory. Riemann zeta function ζ (s) in the complex plane. The color of a point s encodes the value of ζ (s): colors close to black denote values close to zero, while hue encodes the value's argument. In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve ...
Checked. Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted ...
Operation (mathematics) In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and ...
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.