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.

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TopNewestThe 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!

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

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