Practice30 Create account

For which values of n is $x$ ⁿ + aⁿ always divisible by $(x + a)$ ?

Competition practiceNumber System, HCF & LCM

AOnly even n
BOnly odd n
CAll natural n
DOnly prime n

Step-by-Step Solution

Putting

x = - a : (- a)^{n} + a^{n} = 0

only when

n

is odd, so

(x + a)

is a factor only for odd

n

.

Answer: B) Only odd n

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Number System, HCF & LCM practice questions

More Number System, HCF & LCM practice

Which of the following numbers exactly divides (49¹⁵ − 1)?Which of the following exactly divides (17²⁰⁰ − 1)?The number (2⁴⁸ − 1) is exactly divisible by two numbers between 60 and 70. Which are…What is the unit digit of 6374¹⁷⁹³ × 625³¹⁷ × 341⁴⁹¹?How many numbers between 100 and 500 are divisible by both 6 and 8?