How do I prove that 7^n-4^n is divisible by 3?

Algebra

[math]7^n - 4^n = 3m[/math] where [math]m\in N[/math] (m is a set of all natural numbers)

If the equation is true then the equation,

7^(n+1)-4^(n+1) = 3r, where r\in N, must be true.

[math]7(7^n)-4(4^n) = 3r[/math]

Since [math]7^n-4^n =3m[/math], then [math]7^n=4^n+3m.[/math]

So,

[math]7(4^n + 3m) -4(4^n)=3r[/math]

[math]3(4^n) + 3m =3r[/math]

[math]3(4^n + m)=3r[/math]

It is true for all [math]r=4^n+m[/math] which are integer.

Hence, [math]7^n-4^n[/math] is truely divisible by 3 where [math]n\in N[/math].