a triangular array of squares has rows, with one square in the first row, two in the second, and so on. with the exception of the bottom row, each square rests on two squares in the row immediately below (as shown below). emma writes one of the numbers and into each of the squares in the bottom row. she then writes a number into every other square in the array, working from the bottom up, so that the number in each square is the sum of the numbers in the two squares below it. in how many ways could emma write 's and 's into the squares in the bottom row so that the number she writes in the top square is a multiple of ?