Abstract
We obtain a new lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits.
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W. D. Banks, M. Z. Garaev, F. Luca and I. E. Shparlinski, Uniform distribution of fractional parts related to pseudoprimes, Canad. J. Math., to appear.
W. D. Banks and I. E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arith., 112 (2004), 313–332.
J. Bourgain, Estimates on exponential sums related to Diffie-Hellman distributions, Geom. Funct. Anal., 15 (2005), 1–34.
P. Erdős and R. Murty, On the order of a (mod p), Proc. 5th Canadian Number Theory Association Conf., Amer. Math. Soc., Providence, RI, 1999, 87–97.
E. Fouvry and C. Mauduit, Methódes des crible et fonctions sommes des chiffres, Acta Arith., 77 (1996), 339–351.
E. Fouvry and C. Mauduit, Sommes des chiffres et nombres presque premiers, Math. Ann., 305 (1996), 571–599.
K.-H. Indlekofer and N. M. Timofeev, Divisors of shifted primes, Publ. Math. Debrecen, 60 (2002), 307–345.
S. Konyagin, Arithmetic properties of integers with missing digits: distribution in residue classes, Period. Math. Hungar., 42 (2001), 145–162.
S. V. Konyagin, C. Mauduit and A. Sárkőzy, On the number of prime factors of integers characterized by digit properties, Period. Math. Hungar., 40 (2000), 37–52.
F. Luca, Arithmetic properties of positive integers with fixed digit sum, preprint, 2002.
C. Mauduit and A. Sárközy, On the arithmetic structure of sets characterized by sum of digits properties, J. Number Theory, 61 (1996), 25–38.
C. Mauduit and A. Sárközy, On the arithmetic structure of the integers whose sum of digits is fixed, Acta Arith., 81 (1997), 145–173.
F. Pappalardi, On the order of finitely generated subgroups of Q* (mod p) and divisors of p − 1, J. Number Theory, 57 (1996), 207–222.
I. E. Shparlinski, Prime divisors of sparse integers, Period. Math. Hungar., 46 (2003), 215–222.
C. L. Stewart, On the representation of an integer in two different bases, J. Reine Angew. Math., 319 (1980), 63–72.
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Communicated by Attila Pethő
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Shparlinski, I.E. Exponential sums and prime divisors of sparse integers. Period Math Hung 57, 93–99 (2008). https://doi.org/10.1007/s10998-008-7093-3
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DOI: https://doi.org/10.1007/s10998-008-7093-3