we see that there are 9 values for n between 1 and 100.
OR
By the quadratic formula, x2+x−n=(x−x1​)(x−x2​) if and only if x1​,x2​=2−1±1+4n​​. Since every odd square is of the form 1+4n, the answer is the number of odd squares between 1+4⋅1 and 1+4⋅100. There are 9 odd squares in this range, the largest of which is 192.