a. Fermat’s last theorem says that for all integers n > 2, the equation xn + yn = zn has no positive integer solution (solution for which x, y, and z are positive integers). Prove the following: If for all prime numbers p > 2, xp + yp = zp has no positive integer solution, then for any integer n > 2 that is not a power of 2, xn + yn = zn has no positive integer solution.
b. Fermat proved that there are no integers x, y, and z such that x4 + y4 = z4. Use this result to remove the restriction in part (a) that n not be a power of 2. That is, prove that if n is a power of 2 and n > 4, then xn + yn = znhas no positive integer solution.
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