Can anyone explain Fermat's Theorem?

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Juhi Sharma (1527)

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Fermat's Last Theorem states that

xⁿ + yⁿ = zⁿ

has no non-zero integer solutions for x, y and z when n > 2, i.e. It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers.

The restriction n>2 is obviously necessary since there are a number of elementary formulas for generating an infinite number of Pythagorean triples (x,y,z) satisfying the equation for n=2,

x^2+y^2=z^2.

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