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.
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页码：1287 / 1305
页数：19
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