Arithmetic properties of the sequence of derangements

Journal of Number Theory - Tập 163 - Trang 114-145 - 2016
Piotr Miska1
1Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University in Cracow, Poland

Tài liệu tham khảo

Amdeberhan, 2013, Valuations and combinatorics of truncated exponential sums, Integers, 13 Berndt, 2000, On the Brocard–Ramanujan Diophantine equation n!+1=m2, Ramanujan J., 4, 41, 10.1023/A:1009873805276 Bollman, 2010, Fibonacci numbers which are sums of three factorials, Publ. Math. Debrecen, 77, 211, 10.5486/PMD.2010.4700 Cassels, 1986 Dąbrowski, 1996, On the Diophantine equation x!+A=y2, Nieuw Arch. Wiskd., 14, 321 Dąbrowski, 2013, Variations on the Brocard–Ramanujan equation, J. Number Theory, 133, 1168, 10.1016/j.jnt.2012.09.005 Erdős, 1937, Über diophantische Gleichungen der form n!=xp±yp und n!±m!=xp, Acta Litt. Sci. Szeged, 8, 241 Gawron, 2013, A note on the Diophantine equation P(z)=m!+n!, Colloq. Math., 131, 10.4064/cm131-1-5 Grossman, 2002, Sums of factorials in binary recurrence sequences, J. Number Theory, 93, 87, 10.1006/jnth.2001.2718 Guy, 2004 Kurepa, 1973, On the left factorial function !n, Math. Balkanica (N.S.), 1, 147 Legendre, 1830 Luca, 1999, Products of factorials in binary recurrence sequences, Rocky Mountain J. Math., 29, 1387, 10.1216/rmjm/1181070412 Luca, 2002, The Diophantine equation P(n)=m! and a result of M. Overholt, Glas. Mat. Ser. III, 37, 269 Luca, 2010, Factorials expressible as sums of at most three Fibonacci numbers, Proc. Edinb. Math. Soc., 53, 679, 10.1017/S0013091508000874 Marques, 2014, The 2-adic order of the Tribonacci numbers and the equation Tn=m!, J. Integer Seq., 17 Miska, 2015, A note on p-adic valuations of Schenker sums, Colloq. Math., 140, 10.4064/cm140-1-2 Moll, 2012 Narkiewicz, 2003 Serre, 1973 Sun, 2011, On a curious property of Bell numbers, Bull. Aust. Math. Soc., 84, 153, 10.1017/S0004972711002218 Ulas, 2012, Some observations on the Diophantine equation y2=x!+A and related results, Bull. Aust. Math. Soc., 86, 377, 10.1017/S0004972712000512 Wolfram, 2003