A conjecture of Cai-Zhang-Shen for figurate primes says that every integer n
> 1 is the sum of two figurate primes. In this paper we give respectively
equivalent propositions to the conjecture in the cases of even and odd integers
and then confirm the conjecture by considering functions with several
variables.Comment: 12page

Niu, Pengcheng

English

arXiv

A conjecture of Cai-Zhang-Shen for figurate primes says that every integer
$k>1$ is the sum of two figurate primes. In this paper we give an equivalent
proposition to the conjecture. By considering extreme value problems with
constraints about the conjecture in the cases of even and odd integers and
using the method of Lagrange multipliers, we prove the conjecture.Comment: 17page

On a Conjecture of Cai-Zhang-Shen for Figurate Primes

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