1. The problem statement, all variables and given/known data I need to prove two things about the Catalan numbers. The first is that Cn is odd iff n=(2^k)-1 for some positive integer k. The second is that given the matrix A defined by the rule a(i,j)=C(i+j), prove that det A=1. I have not covered determinants in my linear class yet, so I do not have any idea what to do with this one. 2. Relevant equations 3. The attempt at a solution I am assuming that both proceed by induction. The first one seems to be more direct, but I am really lost as to how to proceed with both. Any help or suggestions is greatly appreciated. Thanks a lot!