D. Krachun

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20182020

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math.NT2020

On sums of four pentagonal numbers with coefficients

Dmitry Krachun, Zhi-Wei Sun

The pentagonal numbers are the integers given by $p_{5} (n) = n (3 n - 1) /2 (n = 0, 1, 2, \dots)$ . Let $(b, c, d)$ be one of the triples $(1, 1, 2), (1, 2, 3), (1, 2, 6)$ and $(2, 3, 4)$ . We show that eac…

math.NT2018

On some determinants involving Jacobi symbols

Dmitry Krachun, Fedor Petrov, Zhi-Wei Sun +1

In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer $n \equiv 3 (mod 4)$ , we show that $$(6,1)_n=[6,1]_n=(3,…