## Did Fermat really prove his theorem?

No he did not. Fermat claimed to have found a proof of the theorem at an early stage in his career. Much later he spent time and effort proving the cases n=4 and n=5. Had he had a proof to his theorem earlier, there would have been no need for him to study specific cases.

## Can theorem be wrong?

Originally Answered: Can someone disproves a proven theorem? There is no such thing as a “proven theorem” there is only a “theorem that has a proof”. The proof itself could have flaws in its logic or hidden assumptions which turn out to be untrue.

What does Fermat’s last theorem state?

Fermat’s last theorem, also called Fermat’s great theorem, the statement that there are no natural numbers (1, 2, 3,…) x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2.

Why is Fermat’s little theorem important?

Fermat’s little theorem is a fundamental theorem in elementary number theory, which helps compute powers of integers modulo prime numbers. It is a special case of Euler’s theorem, and is important in applications of elementary number theory, including primality testing and public-key cryptography.

### Is a theorem a truth?

Theoremhood and truth All theorems were proved by using implicitly or explicitly these basic properties, and, because of the evidence of these basic properties, a proved theorem was considered as a definitive truth, unless there was an error in the proof.

### Did Fermat prove this theorem?

Did Fermat prove his theorem? No he did not. Fermat claimed to have found a proof of the theorem at an early stage in his career. Much later he spent time and effort proving the cases n=4 and n=5. This method can actually be used to prove a stronger statement than FLT for n=4, viz, has no non-trivial integer solutions.

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What are the uses of Fermat’s little theorem?

Fermat’s little theorem is a fundamental theorem in elementary number theory, which helps compute powers of integers modulo prime numbers. It is a special case of Euler’s theorem, and is important in applications of elementary number theory, including primality testing and public-key cryptography.

What was Fermi’s Last Theorem?

In number theory, Fermat’s Last Theorem (sometimes called Fermat’s conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.