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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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Abstract  

We estimate multiplicative character sums over the integers with a fixed sum of binary digits and apply these results to study the distribution of products of such integers in residues modulo a prime p. Such products have recently appeared in some cryptographic algorithms, thus our results give some quantitative assurances of their pseudorandomness which is crucial for the security of these algorithms.

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