We are given that n(n +30) a perfect square. What are the possible values of n Hint (a) Suppose that a and a +I are perfect squares. Writing a = 62, a +1 = (b + 5)2 we have l = 2sb + s2 = s(26 + 8) (b) We have d = (n, 30+ n) is one of the divisors of 30. (c) We have n/d and n/d + 30/d are relatively prime integers and n/d(n/d + 30/d) = n(n+30) d2 where the right hand side is an integer and a perfect square. Let S = b2 then n 30 30 + = (b + 8) and s(20 + 8). d d d The possibilities for d, b, and s are very limited.