Seda Albayrak

In this talk, I will talk about use of automata theory in answering problems in number theory. In 1844, Catalan conjectured that the set consisting of natural numbers of the form $2^n+1$, $n \ge 0$ and the set consisting of powers of $3$ has finite...

Christol's theorem (1979), which sets ground for many interactions between theoretical computer science and number theory, characterizes the coefficients of a formal power series over a finite field of positive characteristic $p>0$ that satisfy an...

TBC

In 1979, Erdős conjectured that for k≥9, 2k is not the sum of distinct powers of 3. That is, the set of powers of two (which is 2-automatic) and the 3-automatic set consisting of numbers whose ternary expansions omit 2 has finite intersection. In the...