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mahalex
on April 22, 2023
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Tell HN: 2^4 == 4^2, extended to rationals
If we exclude 0, the only solutions are 2^1 = 1^2 + 1 and 3^2 = 2^3 + 1
nmmnthrowaway
on April 22, 2023
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That is correct. Why are there no others?
mahalex
on April 22, 2023
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Because Catalan’s conjecture.
yarg
on April 22, 2023
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> Catalan's conjecture was proven by Preda Mihăilescu in April 2002.
Cool, so the conjecture's a theorem.
https://xn--uni-gttingen-8ib.academia.edu/PredaMihailescu
hgsgm
on April 22, 2023
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Which has an extremely complicated proof :-(
mahalex
on April 22, 2023
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I wouldn’t call it extremely complicated; it is much simpler than the proof of FLT.
nmmnthrowaway
on April 22, 2023
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Yes, but there is a much simpler proof.
judofyr
on April 22, 2023
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Something related to prime factorization maybe?
AnimalMuppet
on April 22, 2023
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Do tell.
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