## Solution of FLT for $n=4$.

I discussed FLT in an earlier post and stated a problem that if solved FLT for will be deduced from there. Below is a solution to that problem. Assume is a “non-trivial” triple of integers that satisfies (1) . By “non-trivial” we mean “". Obviously we can assume that and are positive. If we show for any such triple, there is another triple satisfying the same equation with a smaller , then using the method of “infinite descent” we get a contradiction, and therefore we can deduce that there is no “non-trivial” solutions for . Now one can show that and are relatively prime. Otherwise you can find a “smaller” solution for the equation (1).(more...)