Innocent-looking problems involving whole numbers can stymie even the most astute mathematicians. As in the case of Fermats last theorem, centuries of effort may go into proving such tantalizing, deceptively simple conjectures in number theory.
Now, Preda Mihailescu of the University of Paderborn in Germany finally may have the key to a venerable problem known as Catalans conjecture, which concerns the powers of whole numbers.
Consider the sequence of all squares and cubes of whole numbers greater than 1, a sequence that begins with the integers 4, 8, 9, 16, 25, 27, and 36. In this sequence, 8 (the cube of 2) and 9 (the square of 3) are not only powers of integers but also consecutive whole numbers.