1. It is always divisible by a-b.The following rules should be remembered as (a^n - b^n) 2. When n is even it is also divisible by a+b. 3. When n is odd it is not divisible by a+b. The following rules should be remembered as (a^n + b^n)1. It is never divisible by a-b. 2. When n is odd it is divisible by a+b. 3. When n is even it is not divisible by a+b. |

Examples 1. Which of the following statements is true about (16^n+1) ? A. It is always divisible by 17. B. It is never divisible by 17. C. It is always divisible by 15. D. It is never divisible by 15. Solution : Since 16^n +1 is in the form a^n+b^n, on the basis of the rules, we know the following A. It is never divisible by 16-1=15. B. When n is odd, it is divisible by 16+1=17. C. When n is even, It is not divisible by 16+1=17. On the basis of the following we can say option D is correct answer. 2. Which of the following statements is true about (11^n-1) ? A. It is always divisible by 10. B. It is always divisible by 12. C. It is divisible by 12 when n is odd. D. It is never divisible by 10. Solution : Since (11^n-1) is in the form of a^n-b^n, on the basis of the rules discussed , we know that 11^n-1 is divisible by 11-1=10 for all values of n.Hence, Option A is the correct answer. |