On arithmetic properties of products and shifted products
Résumé
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.