What is "Fermat's Theorem" ?

Question

What does it actually try to prove ?

Answer 1

Fermat's Last Theorem (sometimes abbreviated as FLT) is one of the most famous theorems in the history of mathematics. It states that:

It is impossible to separate any power higher than the second into two like powers,
or, using more formal mathematical notation:

If an integer n is greater than two, then an + bn = cn has no solutions in non-zero integers a, b, and c.
The 17th-century mathematician Pierre de Fermat wrote in 1637 in his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus: "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.") However, no correct proof was found for 357 years, until it was finally proven using very deep methods by Andrew Wiles in 1995.

This statement is significant because all the other theorems proposed by Fermat were settled, either by proofs he supplied or by rigorous proofs found afterwards. The theorem was not the last that Fermat conjectured, but the last to be proved. The theorem is generally thought to be the mathematical result that has provoked the largest number of incorrect proofs, perhaps because it is easy to understand.

Answer 2

The Fermat's Last Theorem (or Fermat's Great Theorem, or Fermat's Theorem), by Pierre de Fermat, states that there are no solutions for a^n + b^n = c^n where n > 2 and a,b,c and n are all integers.

This doesn't actually "prove." It doesn't even have a practical real-life application. But the thing is that it took years before a complete proof for this seemingly simple statement is created. along with this, Fermat said "I got a truly marvellous proof for it" but it wasn't found. ^_^

That is that.
^_^

Answer 3

Fermat's Last Theorem is described in the other answers, but for completeness It states that if x, y and z are whole numbers and x^n + y^n = z^n, then n<3.
i.e. it works for n = 1
2^1 + 3^1 = 5^1
and for n = 2
3^2 + 4^2 = 5^2
But not for n = 3 or larger.

But he also had other theorems which he did manage to document proof for - the main one is probably Fermat's Little Therorem which states that if p is a prime number, then for any integer a,
a^p = a (mod p)

This means that if you start with a number, multiply it by a, p times, and then subtract a from the result, the final result is divisible by p.

But you were probably looking for his last theorem, not his little one.

Answer 4

Pierre de Fermat's theorem on sums of two squares states that an odd prime number p is expressible as

p = x^2 + y^2
with x and y integers,


For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares.

Answer 5

The statement of Fermat's Last Theorem (FLT for short) is about as simple as any mathematical proposition could be:

The equation has no solution for non-zero integers x, y, and z if n is an integer greater than 2.

Answer 6

do not problem about attempting to coach it. proffessional mathematicians were attempting for decades, with out achievement. The funny tale is that Fermat himself in hardship-free words stated "I have a impressive information that isn't slot in this little margin" yet he under no circumstances instructed anybody what it become... it is why it is so plaguing for different mathematicians. extra to the point, be in a position to communicate intelligently about why it ought to't be proved, or what issues were encountered, and failed proofs of the previous.

Answer 7

its a theorem about fermat

Answer 8

use google.
It proofs that the equation
a^n + b^n = c^n
whith a,b,c,n positive integers has no solutions for n>=3