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/sci/ - Science & Math

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10735256 No.10735256 [Reply] [Original]

I rember to have read somewhere that the equation a^b = b^a + 1 (a,b are positive natural numbers) has only one solution, i.e. (a,b) = (3, 2).
I also remember that this is a conjecture or maybe it was proved but the proof is really difficult.
Does someone know the name of this conjecture/theorem?
Maybe I found it while I was reading something on Erdos, I can't remember.

>> No.10735452

>>10735256
I didn't read your whole post and was like "whelp that's the fakest shiz I've ever seen" when I tried 3 and 4

>> No.10735454

>>10735452
what?

>> No.10735486

>>10735452
same when i plugged in 1 and 2

>> No.10735504

>>10735452
3^4=81
4^3=64
>>10735486
That one's correct.

>> No.10735540
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10735540

>>10735504
>>10735454

>> No.10735760

(a, b) = (2, 1) you retard

>> No.10736080

>>10735760
I was only pretending to be retarded

>> No.10736534

>>10735760
Ok I'm retarded, I reformulate with "the only positive solutions are (2,1) and (3,2)"
Could someone prove this? Or try to find another solution.

>> No.10736571

Not sure, but it might be Catalan's conjecture.

>> No.10736584

>>10735256
No idea, but sounds like something related to modular arithmetic or cryptography.
Also >>10735760