Leírás
Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m23e0027e834ba7d47114e0ff6690fb63
Abstract (Nóra Varga): There are a lot of effective, ineffective and explicit results concerning power values and polynomial values of binomial coefficients. Also, many papers deal with generalizations of these problems, involving polygonal numbers and pyramidal numbers. In this talk we show effective and ineffective theorems concerning polynomial values of figurate numbers. Our results yield common extensions and generalizations of several previous theorems from the literature (joint work with Lajos Hajdu).
Abstract (László Szalay): Let Fn denote the nth Fibonacci number. The well known divisibility properties F(n-ε)/2|(Fn-1) for some ε∈{-2,-1,1,2} and F(n-δ)/2|(Fn2-1) for some δ∈{1,2} induce the following question. Which Fibonacci numbers divide Fn3-1=(Fn-1)(Fn2+Fn+1)? We show that if Fk|Fn2+Fn+1, then k∈{4,7}. Analogously, if Lk|Fn2+Fn+1, where Lk is the kth Lucas number, then k∈{2,4}. This is a joint result with F. Luca and P. Pongsriiam.