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Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between and for every positive integer . The conjecture is one of Landau's problems (1912) on prime numbers, and is one of many open problems on the spacing of prime numbers. Unsolved problem in mathematics: Does there always exist at least one prime ...
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 Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, and proved by Melfi in 1996: every even number is a sum of two practical numbers. Harvey Dubner proposed a strengthening of the Goldbach conjecture that states that every even integer greater than 4208 is the sum of two twin ...
Landau's problems. At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. They are as follows:
Word problem (mathematics) In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Büchi's problem. : Is every sufficiently large sequence of square numbers with constant second difference necessarily a sequence of consecutive square numbers? In number theory, Büchi's problem, also known as the n squares' problem, is an open problem named after the Swiss mathematician Julius Richard Büchi. It asks whether there is a ...
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