Divided 124 into four parts which are in AP such that the product of the first and fourth part is 128 less than the products of the seconds and third part?

Let the four parts be (a - 3d), (a - d), (a + d) and (a + 3d).
(a - 3d) + (a - d) + (a +d ) + (a + 3d) = 124
⇒ a = 31
Also, (a - 3d) (a + 3d) = (a - d) (a + d) - 128
⇒ a² - 9d² = a² - d² - 128
⇒ 8d² = 128
⇒ d = 4
a = 31, d = 4
So, the four parts are 19, 27, 35, 43.