Number of prime divisors in a product of consecutive integers
Shanta Laishram, T. N. Shorey (2004)
Acta Arithmetica
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Shanta Laishram, T. N. Shorey (2004)
Acta Arithmetica
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S. D. Adhikari, G. Coppola, Anirban Mukhopadhyay (2002)
Acta Arithmetica
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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.
Filip, Ferdinánd, Liptai, Kálmán, Tóth, János (2006)
Annales Mathematicae et Informaticae
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Chen, Yong-Gao, Fang, Jin-Hui (2008)
Integers
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K. Szymiczek (1964)
Colloquium Mathematicae
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Davis, Simon (2003)
International Journal of Mathematics and Mathematical Sciences
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Zhou, Weiyi, Zhu, Long (2009)
Integers
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Hiroyuki Okazaki, Yasunari Shidama (2008)
Formalized Mathematics
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In the [20], it had been proven that the Integers modulo p, in this article we shall refer as Z/pZ, constitutes a field if and only if Z/pZ is a prime. Then the prime modulo Z/pZ is an additive cyclic group and Z/pZ* = Z/pZ{0is a multiplicative cyclic group, too. The former has been proven in the [23]. However, the latter had not been proven yet. In this article, first, we prove a theorem concerning the LCM to prove the existence of primitive elements of Z/pZ*. Moreover we prove the...
Clifford Queen (1974)
Acta Arithmetica
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Florian Luca, Francesco Pappalardi (2007)
Acta Arithmetica
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J. Turk (1980)
Journal für die reine und angewandte Mathematik
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Jiahai Kan (2004)
Acta Arithmetica
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K. Ramachandra (1971)
Acta Arithmetica
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