On variants of Pillai’s problems with polynomials

Activity: Talk or presentationTalk at conference or symposiumScience to science


In this talk I will discuss several polynomial variants of some well-known Pillai's Diophantine problems. In particular, in my focus is the equation
in complex polynomials f,p,q with f nonzero and p and q nonconstant, nonzero complex numbers ai,bi and positive integers ni,mi. Of particular importance is the special case a1=a2=1 and b1=b2=−1 corresponding to a well-studied Pillai's Diophantine equation an1−bm1=an2−bm2 in positive integers ni,mi,a,b with a>1 and b>1.
Furthermore, I will show that for nonconstant coprime complex polynomials p and q, the number of solutions (n,m)∈N2 of 0≤deg(p(x)n−q(x)m)≤d is asymptotically equal to d2/(degpdegq) as d→∞, as well as consider a generalization of this problem where the powers of polynomials are replaced by the sums of powers of polynomials.
Period16 Jun 2022
Event title7th Croatian Mathematical Congress
Event typeConference
LocationSplit, CroatiaShow on map