10^m-10^n is always a factor of 9 if m and n are positive integers?
Can someone please give me a proof for this? I don’t know how to prove that that is true.
Can someone please give me a proof for this? I don’t know how to prove that that is true.
2 Answers
See proof in explanation.
The proof works with the modulo operator.
Explanation:
Please refer to a Proof in the Explanation.
Explanation:
If
So, we let,
Then, either
We will prove the assertion for
The Proof for
Now,
Now,
Now, expanding
which clearly shows that
Hence, the Proof.
Enjoy Maths.!