Question

The HCF of a^m + b^m and a^n - b^n , where m is odd positive integer and n is even positive integer is ??​

Answer 1

Given:

a^m + b^m and a^n - b^n.

To find:

HCF of a^m + b^m and a^n - b^n

Solution:

1) In a^m + b^m where m in odd integer so the expression must have the factor a+b.

2) In a^n - b^n where n is even integer so the expression must have the factor a+b and a-b.

3) As per the above steps the common factor is a+b

Hence, HCF of a^m + b^m and a^n - b^n is a+b