Proof of fermats theorem in some simple way

Fermats theorem

Note by Hardik Chandak
5 years, 10 months ago

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Are you looking for a simple proof of Fermat's Little Theorem or Fermat's Last Theorem or one of the many other theorems named after Fermat?

- 5 years, 10 months ago

FERMATS LAST THEOREM

- 3 years, 4 months ago

I'm pretty sure Fermat's Last Theorem

- 5 years, 10 months ago

Fermat's Little Theorem can be proved using induction.

- 5 years, 10 months ago

Can u prove it by induction plz show?

- 5 years, 10 months ago

It's not by induction, but an easy proof of Fermat's little theorem would be that $x^p \equiv (1+1+1+...+1)^p \equiv (1^p+1^p+...+1^p) \equiv x \pmod p$ with $x$ times number $1$. This is possible because in Pascal's triangle on prime rows the numbers are multiples of p except for the first and last terms which are $1$. This can be easily proven by using binomial formula.

- 5 years, 10 months ago

Okay get your calculators and try this:

$\sqrt[12]{1782^{12}+1841^{12}}$

$=1922$ right?

So this implies that ${1782^{12}+1841^{12}=1922^{12}}$

Does this disprove Fermat's Last Theorem?

Of course not!

The calculator is wrong.

- 5 years, 10 months ago

BTW: A quick check to see that $1782^{12}+1841^{12} \neq 1922^{12}$ is to note that the left side is odd whereas the right side is even.

- 5 years, 10 months ago

Took some time to realize... The actual answer is $1921.99999995586722540291132837029507293441170657370868230...$ Unfortunately, most calculators round the answer.

- 5 years, 10 months ago

If I remember correctly, that "equation" was from a Homer Simpson episode.

- 5 years, 10 months ago

I can give you a proof .

- 4 years, 8 months ago