Find all possible integer values of n such that 2n^2 + 2n + 38 is a 4-digit number with all 4 digits equal.
2n^2 + 2n + 38 =
2 ( n^2 + n + 19)
Since this is a multiple of 2 the only possibilities are
2222, 4444, 6666 or 8888
There are no integer n's such that
2n^2 + 2n + 38 = any of these