In the equality 4 + 5 + 6 + 7 + 8 = 9 + 10 + 11, the sum of the five consecutive integers from 4 upwards is equal to the sum of the next three consecutive integers.

If the the variables n, k and c represent positive integers, then show that the sum of the n+k consecutive integers from c upwards is equal to the sum of the next n consecutive integers iff 2n² + k = 2ck + k².