Good day to the MHF. Here's my problem
Find all integer solutions to
Just making sure my solution is complete
By CRT, we can break this up to
And now we deal with each separately
we use FLT to simplify:
. Solves to give
Now dealing with
, we solve this via guesswork
So now we use CRT to solve
Solve to get
And a solution to our original equation is
Is this all the solutions or am I missing some? If so, where is te error in my method preventing me from obtaining the others?
Thanks in advance for the help.