Rob Tijdeman (Leiden): The Prouhet-Tarry-Escott problem, indecomposability of polynomials and Diophantine equations

Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m6048be44031cc12a05c3f26c0b0cf041

Abstract: In this talk we show how the subjects mentioned in the title are related. First we study the structure of partitions of A ⊆ {1,...,n} in k-sets such that the first k-1 symmetric polynomials of the elements of the k-sets coincide. Then we apply this result to derive a decomposability result for the polynomial fA(x):=Πa∈A(x-a). Finally we prove two theorems on the structure of the solutions (x,y) of the Diophantine equation fA(x)=P(y) where P(y)∈ℚ[y]. This is a joint work with L. Hajdu and Á. Papp.