Question

What is the smallest integer that can be added to -2m3 − m + m2 + 1 to make it completely divisible by m + 1

Answer 1

When divided by 2 we get perfect square 
(2^n * 3^m) / 2 = 2^(n-1) * 3^m is a perfect square 
(n-1) and m are divisible by 2
 When divided by 3 we get perfect cube 
(2^n * 3^m) / 3 = 2^n * 3^(m-1) is a perfect cube 
n and (m-1) are divisible by 3 
(n-1) divisible by 2 & n divisible by 3 → n = 3 
m divisible by 2 & (m-1) divisible by 3 → m = 4 
Number = 2³ * 3⁴ = 648 
648/2 = 324 = 18² 
648/3 = 216 = 6³ 
ANSWER: 648