%0 Book Section
%T On arithmetic properties of products and shifted products
%+ Institut de Mathématiques de Marseille (I2M)
%+ Department of Algebra and Number Theory [Budapest]
%A Rivat, Joel
%A Sárközy, András
%Z In Honor of Helmut Maier’s 60th Birthday
%@ 978-3-319-22239-4
%B Analytic Number Theory
%E Carl Pomerance • Michael Th. Rassias
%I Springer International Publishing
%P 345-355
%8 2015
%D 2015
%R 10.1007/978-3-319-22240-0_21
%K Product of sequences
%K Shifted products
%K Digit properties
%K Squares
%K Multiplicative characters
%K Large sieve
%Z Computer Science [cs]
%Z Computer Science [cs]/Cryptography and Security [cs.CR]
%Z Mathematics [math]/Number Theory [math.NT]Book sections
%X Let A and B be large subsets of {1…,N}. Arithmetic properties of the products ab, resp. of the shifted products ab + 1 with a∈A, b∈A  are studied. In particular, it is shown that the sum of digits of the products ab is well distributed, and the size of the subsets A,B∈{1…,N} with the property that ab + 1 is always squarefree is estimated.
%G English
%L hal-01260187
%U https://hal.science/hal-01260187
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-