Question

If n is a natural number, then $9^{2n} - 4^{2n}$ is always divisible by
(a) 5
(b) 13
(c) both 5 and 13
(d) None of these

Answer 1

Answer:

9²ⁿ– 4²ⁿ  is always divisible by both 5 and 13.  

Among the given options option (c) both 5 and 13 is the correct answer.

Step-by-step explanation:

Given :  

n is a natural number

If we put n = 1 , then  

9²ⁿ– 4²ⁿ  = 9² - 4²  

= 81 - 16  

= 65

65  is always divisible by both 5 and 13.

If we put n = 2 then,

9²ⁿ– 4²ⁿ  = 9⁴ - 4⁴  

= 6561 - 256

= 6305

6305 is always divisible by both 5 and 13.

Hence, 9²ⁿ– 4²ⁿ  is always divisible by both 5 and 13.  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

When n is equal to 1 then 9 2n - 4 2n is divisible by 5 or 13. n could be any natural number 9 2n - 4 2n will be divisible by 5 or 13 only.

so both 5 and 13.