# Prime Number Powers of Integers and Fermat's Last Theorem

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e2m2a
TL;DR Summary
Need understanding of an integer to a perfect power raised to the power of a prime number as it relates to Fermat's Last Theorem.
From my research I have found that since Fermat proved his last theorem for the n=4 case, one only needs to prove his theorem for the case where n=odd prime where c^n = a^n + b^n. But I am not clear on some points relating to this. For example, what if we have the term (c^x)^p, where c is an integer, x = even integer, and p = odd prime. Then we can express this term as c^(xp) and we would have c^(xp)=a^n +b^n. Clearly, xp is no longer an odd prime. So, does this mean to prove Fermat's Last Theorem for the case where n=odd prime, then neither of the bases c,a,b themselves can be an integer that is raised to an even numbered power?