Affiliation:
1. The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, WITS 2050, Johannesburg, South Africa
2. Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, Mexico
Abstract
We prove that the Diophantine equation [Formula: see text] has only finitely many positive integer solutions k, p1, …, pk, r1, …, rk, where p1, …, pk are distinct primes. If a positive integer n has prime factorization [Formula: see text], then [Formula: see text] represents the number of ordered factorizations of n into prime parts. Hence, solutions to the above Diophantine equation are designated as prime-perfect numbers.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory