This proof demonstrates that the cube of a natural number cannot be expressed as an incomplete binomial, showing implications for Fermat's Last Theorem.
A simple proof of Fermat’s Last Theorem (FLT) for the cube is obtained using the binomial expansion formula. The difference of two natural numbers having equal natural powers necessarily has a representation according to the formula of an incomplete binomial. It is proved that the cube of a natural number cannot be represented as anincomplete binomial, which means a simple proof of FLT for n = 3 is obtained.
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Kurmet Sultan (2026) studied this question.
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