If m and n are not prime to each other, the possible number of common roots of the equations $$x^m-1=0, x^n-1=0$$ is​

Correct option is A

Given:
Two equations:
​$$x^m-1=0, x^n-1=0$$​​
And m and n are not coprime, i.e., they have a common factor greater than 1.

Formula:
The number of common roots = number of solutions to x^d - 1 = 0, where d = GCD of m and n

Solution:

The roots of  $$x^m-1=0$$​ are the m-th roots of unity (complex numbers on the unit circle spaced evenly).

Similarly, $$x^n-1=0$$​ has n-th roots of unity.

If m and n are not coprime, then GCD(m, n) = d > 1

Therefore, both equations have all the d-th roots of unity in common.

This means the number of common roots is more than one — exactly d in number.

Final Answer:
The possible number of common roots is more than one