primes and only primes.?

Question

I think in fermats last theorem we have to do the work for powers which are primes or the factors of the power is the prime with the same value such as 4(2*2),49(7*7), Because for non prime powers such as 21 we have to prove only the cubic case or the case for fifth power & if we prove the case of fifth power alone then the case of power 25(5*5) or 125(25*5) is getting proved by itself.Similarly if we prove the 4th power case then the other cases where the factors of the power is only two is getting proved.
In the equation a^(n)-b^(n)=x^(n) or x^(n)+b^(n)=a^(n){fermats last theorem}One more thing is there in it that if "a" has to be even then either "x" & "b" has to be either both odd or both even and lastly we will see that "a" will always be odd to make "x" and "b" natural.
it is obvious as
a^(n)-b^(n)=c^(2)-d^(2) like
7^(3)-4^(3)=140^(2)-139^(2) &
x^(n)=z^(2)-y^(2) like
3^(3)=14^(2)-13^(2).
it is all for natural values of a,b,c,d,x,z,y & of course n.
Identify the primes.

Answer 1

Yes, you are right. To prove Fermat's last theorem, you only have to show it for n either 4 or a prime. The rest of what you say is garbage, though.

Answer 2

It is so obious than in any equation : a + b = c, that if c is even than eithewr a and b even or a and b odd
there is no question , just a long long obvious sory.

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