Question

if n is an odd positive integer then an + bn is divisible by
a) a²+b²
b) a+b
c) a-b
d) none of these​

Answer 1

Given : n is odd positive integer

aⁿ + bⁿ

To find : aⁿ + bⁿ  is divisible by

a) a²+b²

b) a+b

c) a-b

d) none of these​

Solution:

aⁿ + bⁿ

n is  odd positive integer

then aⁿ + bⁿ  is divisible by   a + b

Let say  aⁿ + bⁿ  is a polynomial

and divisible by a - k

=> a = k  

kⁿ + bⁿ = 0

kⁿ = -bⁿ

=> k = - b   as n is odd positive integer

aⁿ + bⁿ  is  divisible by  a -(-b)  = a + b

so a+ b is the the correct option

Learn More:

on dividing x3-3x2+x+2 by a polynomial g(x),the quotient and ...

brainly.in/question/3135153

Divide 9x^3+3x^2-5x+7 by (3x-1) write the quotient and remainder ...

brainly.in/question/6190809

Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1 ...

brainly.in/question/4743553