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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), [5] or as wondrous numbers. [6] Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such ...
"Some problems on the prime factors of consecutive integers II" (PDF). Proceedings of the Washington State University Conference on Number Theory: 13– 21. Grimm, C. A. (1969). "A conjecture on consecutive composite numbers". The American Mathematical Monthly. 76 (10): 1126– 1128. doi:10.2307/2317188. JSTOR 2317188. Guy, R. K. "Grimm's ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
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.
The Pillai sequence tracks the numbers requiring the largest number of primes in their greedy representations. [31] Similar problems to Goldbach's conjecture exist in which primes are replaced by other particular sets of numbers, such as the squares: It was proven by Lagrange that every positive integer is the sum of four squares.
Disproved by Georg Cantor who showed that there are so many transcendental numbers that it is impossible to make a one-to-one mapping between them and the algebraic numbers. In other words, the cardinality of the set of transcendentals (denoted ℶ 1 {\displaystyle \beth _{1}} ) is greater than that of the set of algebraic numbers ( ℵ 0 ...
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 .