Goldbach’s conjecture in max-algebra

Peter Szabó ()
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Peter Szabó: Technical University of Košice

Computational Management Science, 2017, vol. 14, issue 1, No 5, 89 pages

Abstract: 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 $$a\oplus b=\max \{a,b\}$$ a ⊕ b = max { a , b } and $$a\otimes b=a+b$$ a ⊗ b = a + b .

Keywords: Max-algebra; Triangular Toeplitz matrix; Goldbach’s conjecture (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10287-016-0268-z

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