Prime divisors of -binomial coefficients
F. T. Howard (1972)
Rendiconti del Seminario Matematico della Università di Padova
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F. T. Howard (1972)
Rendiconti del Seminario Matematico della Università di Padova
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P. Erdös, C. Lacampagne, J. Selfridge (1988)
Acta Arithmetica
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Kilford, L.J.P. (2004)
International Journal of Mathematics and Mathematical Sciences
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Guerin, E.E., Buschman, R.G. (1976)
Portugaliae mathematica
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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...
Luca, Florian (2001)
Divulgaciones Matemáticas
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Brad Wilson (1998)
Acta Arithmetica
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Andrzej Rotkiewicz (2005)
Acta Mathematica Universitatis Ostraviensis
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We use the properties of -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.