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Unsolved problems in number theory
The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences, arithmetic functions and the greatest prime factor func- tion and mixed problems.
On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
This series focuses on problems of the first type, i.e., on constructing and testing, more exactly, on apriori or, as Knuth calls it, " theoretical " testing.
On finite pseudorandom binary sequences VII: The measures of pseudorandomness
where the maximum is taken over all D = (d1, . . . , dk) and M such that M + dk ≤ N . 2000 Mathematics Subject Classification: Primary 11K45.
A complexity measure for families of binary sequences
It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity, and the cardinality of the smallest family achieving a prescibed f- complexity and multiplicity is estimated.
On the residues of products of prime numbers
V(x,x) =2 x(n) A (n) n<x For k = 2, 3, . . , x ~ 2, (a, q) = 1, we denote the number of solutions of PlP2 . . . pk-a (mod q), p,<x, p2Sx, . . .,Pk<x by f (x, a, k) ; in particular, we put F(a, k) = f
On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits
We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We