Question Of The Day

⦁ If x is a natural number greater than 17 and (x + 1)(x + 2)(x + 3)(x + 4) + c is perfect square, then the least non negative value of c is

a) 0

b) 1

c) 4

d) none of these

Ans: b) 1

[Details] (x2 + 5x + 4)(x2 + 5x + 6) + c = (x2 + 5x + 4)2 + 2(x2 + 5x + 4) + c. Hence least c = 1