Problems and Results in Combinatorial Analysis and Combinatorial Number Theory

In this note,first of all, I state a few older problems whose solution or partial solution is long overdue and which in some cases were neglected. I also state a few more recent questions. I prove in detail a recent theorem of Selfridge and myself and of Ulam and myself. I try to give as exact references as possible but I am willing (and eager) to correct any mistakes which are pointed out to me .