I have the question prove by induction that 5^2n-4^n is divisible by 7.
In proving p(n+1) implies P(n) I have got:
(5^2n-4^n)+ 21(5^2n-4^n) is divisible by 7 by inductive hypothesis and since 21 is divisible by 7
Just wondering if this argument holds or if anyone has any ideas?
P(k)
is divisible by 7
P(k+1)
is also divisible by 7.
You can attempt to prove that being divisible by 7 causes to be divisible by 7.
This then means that if your formula is true for some n=k, it's automatically true for the next n=k+1.
Hence, if it's then true for n=1, it's true for n=2, 3, 4, 5, 6, 7, 8, to infinity.
We write this "in terms of" to get
Hence, if really is divisible by 7,
then, since 21 is (7)3
will also be divisible by 7.