Goldston, D.A. and Graham, S.W. and Panidapu, A. and Pintz, János and Schettler, J. (2021) Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II. JOURNAL OF NUMBER THEORY, 221. pp. 222-231. ISSN 0022-314X
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Official URL: http://doi.org/10.1016/j.jnt.2020.06.002
Abstract
We show that for any positive integer n, there is some fixed A such that d(x)=d(x+n)=A infinitely often where d(x) denotes the number of divisors of x. In fact, we establish the stronger result that both x and x+n have the same fixed exponent pattern for infinitely many x. Here the exponent pattern of an integer x>1 is the multiset of nonzero exponents which appear in the prime factorization of x. © 2020 The Author(s)
| Item Type: | Article |
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| Additional Information: | Export Date: 17 August 2020 CODEN: JNUTA Correspondence Address: Schettler, J.email: jordan.schettler@sjsu.edu Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, K 119528 Funding text 1: Research supported by the National Research Development and Innovation Office, NKFIH, K 119528. |
| Uncontrolled Keywords: | ERDOS; Small gaps; Almost prime; Divisor; Exponent pattern; Mirsky; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 28 Apr 2021 18:35 |
| Last Modified: | 28 Apr 2021 18:35 |
| URI: | http://real.mtak.hu/id/eprint/124680 |
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