Let $$x= 55^{100} + 55^{101} + 55^{102}$$​. Which of the following prime number is NOT a factor of x ?

Correct option is A

Given:

​$$x= 55^{100} + 55^{101} + 55^{102}$$​​

Solution:

​$$x= 55^{100} + 55^{101} + 55^{102}$$​​

​$$x= 55^{100}(1 + 55^1 + 55^2)$$​​

​$$x= 55^{100} ( 1 + 55 + 3025)$$​​

​$$x= 55^{100} ( 3081)$$​​

Factor of $$55^{100}$$​ are factors of 55 = 5 and 11

Factors of 3081 =$$3 \times 13\times 79$$​​

Hence 71 is not a factor of $$x= 55^{100} + 55^{101} + 55^{102}$$​​