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## 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.

**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.