Some questions

I've red some information about Femat. There was 2 interesting theorems, for which I can't find proof in the internet. So if anyone has some ideas how to proof that and can share them - thanks in advance.

1) 26 is the only number between perfect square and cube (25 and 27).

2) Every prime, that has reminder 1 when divised by 4 is sum of two squares. I tried to prove that, but i stucked up.

#NumberTheory

Easy Math Editor

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Comments

The first is fittingly named Fermat's sandwich theorem, and the second is Fermat's 4n + 1 theorem.

I have never heard of the first theorem before this post; it's quite fascinating!

Zach Abueg - 3 years, 11 months ago

If anyone want the proofs of these theorems, i've found recently them in the book of Edawrds "Last Fermat's Theorem"

Sardor Yakupov - 3 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$