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# Proof of fermats theorem in some simple way

Fermats theorem

Note by Hardik Chandak
4 years, 1 month 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?

- 4 years, 1 month ago

FERMATS LAST THEOREM

- 1 year, 7 months ago

I'm pretty sure Fermat's Last Theorem

- 4 years, 1 month ago

Fermat's Little Theorem can be proved using induction.

- 4 years, 1 month ago

Can u prove it by induction plz show?

- 4 years, 1 month 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.

- 4 years, 1 month ago

I can give you a proof .

- 2 years, 11 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.

- 4 years, 1 month 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.

- 4 years, 1 month ago

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

- 4 years, 1 month ago

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

- 4 years, 1 month ago