On the equations φ(n) = φ(n plus k) and φ(p-1) = φ(q-1)

被引：0

作者：

Kim, Sungjin ^{[1
,2
]}

机构：

[1] Calif State Univ Northridge, 18111 Nordhoff St, Northridge, CA 91330 USA

[2] Santa Monica Coll, 1900 Pico Blvd, Santa Monica, CA 90405 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2021年 / 17卷 / 06期

关键词：

Prime; shifted prime; Euler function; coincidence; PRIMES; NUMBER; GAPS;

D O I：

10.1142/S1793042121500366

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exists positive even integer k such that phi(n) = phi(n + k) holds for infinitely many n. We also prove various estimates on number of solutions to phi(p - 1) = phi(q - 1) for distinct primes p and q.

引用

页码：1287 / 1305

页数：19

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