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- Title
Goldbach's conjecture in max-algebra.
- Authors
Szabó, Peter
- Abstract
The Goldbach conjecture is one of the best known open problems in number theory. It claims that every even integer greater than 2 can be written as the sum of two primes. The present paper formulates a max-algebraic claim that is equivalent to Goldbach's conjecture. The max-algebraic analogue allows examination of the conjecture by the methods of max-algebra. A max-algebra is an algebraic structure in which classical addition $$+$$ and multiplication $$\times $$ are replaced by the operations maximum $$\oplus $$ and addition $$\otimes $$ , in other words $$a\oplus b=\max \{a,b\}$$ and $$a\otimes b=a+b$$ .
- Subjects
GOLDBACH conjecture; ALGEBRAIC equations; INTEGERS; ORDERED algebraic structures; MULTIPLICATION
- Publication
Computational Management Science, 2017, Vol 14, Issue 1, p81
- ISSN
1619-697X
- Publication type
Article
- DOI
10.1007/s10287-016-0268-z