Let , and let . Prove that the last n digits of are the same as the last n digits of .
I just got it!!
We need to prove that is divisible by .
, which is divisible by 10.
So, the statement is true for n = 1.
Let the statement be true for n.
is divisible by .
is divisible by .
is divisible by 10. (As both and end with 5.)
So, is divisible by . This completes the proof.