Find all integers n such that n^3 = (n - 1)^3 + 37.
(n - 1)3 = n3 - 3n2 + 3n - 1
n3 = (n - 1)3 + 37 ---> n3 = ( n3 - 3n2 + 3n - 1 ) + 37
n3 = n3 - 3n2 + 3n - 1 + 37
3n2 - 3n - 36 = 0
3( n2 - 3n 12 ) = 0
n2 - n + 12 = 0
(n - 4)(n + 3) = 0
Either n = 4 or n = -3
