Fred wrote [of the Wikipedia article on Zeckendorf's theorem]: << Also mentioned there is a "Fibonacci product", . . . with x = \sum_i a_i F_i, y = \sum_j b_j F_j, (*) x(*)y = \sum_{i,j} a_i b_j F_{i+j} . Knuth reputedly proved this operation to be associative, which Wikipedia finds surprising. Apparently it follows immediately from . . . . . . --- so after all, Knuth's theorem is surprising!
I, too, first thought this associativity obvious, merely because addition (of indices) is associative . . . but this is specious (I think) since there's nothing to guarantee the RHS of (*) is in Zeckendorf form (which requires no repeated or consecutive indices). --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele