On arithmetic properties of products and shifted products

Joel Rivat (1) , András Sárközy (2)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Algebra and Number Theory [Budapest]

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.

Mots clés: Product of sequences; Shifted products; Digit properties; Squares; Multiplicative characters; Large sieve

Domaines: Informatique [cs]; Cryptographie et sécurité [cs.CR]; Théorie des nombres [math.NT]

Joel Rivat, András Sárközy. On arithmetic properties of products and shifted products. Carl Pomerance • Michael Th. Rassias. Analytic Number Theory, Springer International Publishing, pp.345-355, 2015, 978-3-319-22239-4. ⟨10.1007/978-3-319-22240-0_21⟩. ⟨hal-01260187⟩