Question

Show that ab is a factor of (a + b)^n - (a^n + b^n) for a & b are coprime using factor theorem.​

Answer 1

Step-by-step explanation:

a and b are coprime.

So a+b has no common factor.

f(a, b)=(a+b)^n-a^n-b^n

If ab is a factor then

f(ab)=0

f(ab)=(ab+ab)^n-(ab^n+ab^n)

=(2ab)^n-(2ab)^n

=0

So ab is a factor