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Goldbach’s conjecture in max-algebra

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  • Peter Szabó

    (Technical University of Košice)

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 .

Suggested Citation

  • Peter Szabó, 2017. "Goldbach’s conjecture in max-algebra," Computational Management Science, Springer, vol. 14(1), pages 81-89, January.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:1:d:10.1007_s10287-016-0268-z
    DOI: 10.1007/s10287-016-0268-z
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