Question

If n is an integer greater than or equal to 21, then n^3 - 4n is always divisible by

Answer 1

x655965885855!889999=85555

Answer 2

Step-by-step explanation:

Given If n is an integer greater than or equal to 21, then n^3 - 4n is always divisible by

• So we have n^3 – 4n
•   We can write this as n(n^2 – 4)
•                               n(n + 2)(n – 2)
• So (n – 2) n (n + 2) forms a 3 integers A.P with difference of 2.
• Now assume two cases:
•                n is divisible by 3
•                n is not divisible by 3
• So if n is divisible by 3 nothing is to be proved.
• Now if n is not divisible by 3, there are two possibilities, Remainder is either 1 or 2.
• So if n is divisible by 3 and remainder is 1 then n + 2 is always divisible by 3
• So if remainder is 2, then n – 2 is always divisible by 3

Reference link will be

https://brainly.in/question/5875830