Description
Abstract: In the talk we present various results concerning the total
multiplicative primitivity of value sets of integer polynomials. We give
a complete description of such polynomials whose value set in the set of
positive integers is totally m-primitive. We also provide results
concerning the case where some elements of the value sets may be
omitted. In the quadratic case our results into this direction are
sharp. Further, we give a multiplicative analogue of a result of Sarkozy
and Szemeredi concerning changing elements of the set of shifted k-th
powers {1+1,2^k+1,...,x^k+1,...} (related to a conjecture of Erdos),
which is nearly sharp.
In our proofs we combine several tools from Diophantine number theory, a
classical theorem of Wiegert on the number of divisors of positive
integers and a theorem of Bollobas on the Zarankiewicz function. The
presented new results are joint with A. Sarkozy.
For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).