Question

76^n - 66^n, where n is an integer greater than zero, is divisible by?

Answer 1

$\underline{\textsf{To find:}}$

$\textsf{Factor of}\;\mathsf{76^n-66^n}$

$\underline{\textsf{Solution:}}$

$\textsf{We know that, the identity}$

$\boxed{\mathsf{a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+...........+ab^{n-2}+b^{n-1})}}$

$\mathsf{76^n-66^n}\;\textsf{can be written as}$

$\mathsf{76^n-66^n=(76-66)(76^{n-1}+76^{n-2}(66)+...........+(76)(66)^{n-2}+(66)^{n-1})}$

$\mathsf{76^n-66^n=(10)(76^{n-1}+76^{n-2}(66)+...........+(76)(66)^{n-2}+(66)^{n-1})}$

$\implies\mathsf{76^n-66^n}\;\textsf{is a multiple of 10}$

$\therefore\mathsf{76^n-66^n}\;\textsf{is divisible by10}$