Arithmetic functions over rings with zero divisors.
Ruangsinsap, Pattira, Laohakosol, Vichian, Udomkavanich, Pattanee (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Ruangsinsap, Pattira, Laohakosol, Vichian, Udomkavanich, Pattanee (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Y.-F. S. Pétermann (2004)
Acta Arithmetica
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Gintautas Bareikis, Algirdas Mačiulis (2012)
Acta Arithmetica
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Xavier Benveniste (1984)
Compositio Mathematica
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Bell, Howard E., Guerriero, Franco (1990)
International Journal of Mathematics and Mathematical Sciences
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S. Ebrahimi Atani, M. Shajari Kohan (2011)
Discussiones Mathematicae - General Algebra and Applications
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L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.
Alkhamees, Yousif (1994)
International Journal of Mathematics and Mathematical Sciences
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Milosav M. Marjanović (2005)
The Teaching of Mathematics
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Shi-Chao Chen, Yong-Gao Chen (2004)
Colloquium Mathematicae
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We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.
L. Hajdu, N. Saradha (2010)
Acta Arithmetica
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Florian Luca, Carl Pomerance (2015)
Acta Arithmetica
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Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n) - n, the sum of proper divisors of n.
Prapanpong Pongsriiam, Robert C. Vaughan (2015)
Acta Arithmetica
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Bell, Howard E. (1988)
International Journal of Mathematics and Mathematical Sciences
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S. D. Adhikari, G. Coppola, Anirban Mukhopadhyay (2002)
Acta Arithmetica
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Titu Andreescu, Florian Luca, M. Tip Phaovibul (2016)
Acta Arithmetica
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We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
Friedemann Lucius (1998)
Manuscripta mathematica
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