# Thread: Hints to prove |6^(2n)-5^m| cannot equal 9.

1. ## Hints to prove |6^(2n)-5^m| cannot equal 9.

This is the last step to a problem I've been working on, but I have not had many ideas on how to finish this last step. n and m are positive integers. I was easily able to prove that the above could not equal 1, but I'm not sure what to apply now. Thanks.

|6^(2n)-5^(m)|=9 can be reduced to 5^(m)-6^(2n)=9.

2. ## Re: Hints to prove |6^(2n)-5^m| cannot equal 9.

Originally Posted by eulcer
This is the last step to a problem I've been working on, but I have not had many ideas on how to finish this last step. n and m are positive integers. I was easily able to prove that the above could not equal 1, but I'm not sure what to apply now. Thanks.

|6^(2n)-5^(m)|=9 can be reduced to 5^(m)-6^(2n)=9.
If n>0 then $6^{2n}$ is a multiple of 9 but $5^m$ is not.