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2018-03-15, 16:10   #10
JeppeSN

"Jeppe"
Jan 2016
Denmark

25×5 Posts

Quote:
 Originally Posted by VBCurtis Your OP never mentioned a and b should be prime. I don't see why "1 is not prime" is relevant. Do you mean to now require a>b>1?
No. I wanted to forbid $$1 = 1^{16384} + 0^{16384}$$ as another trivial "solution".

I do not want any trivial solutions.

I know $$(a, b) = (67234, 1)$$ gives an acceptable solution ($$b=1$$ is allowed), but it is certainly not minimal (although we do not have the proof until someone gives an example (EDIT: axn's first post in this thread already gave examples)).

Nitpicking is fine, but hopefully everyone sees I am just asking for the equivalent of $$72^{8192} + 43^{8192}$$ with exponents $$16384$$.

/JeppeSN

Last fiddled with by JeppeSN on 2018-03-15 at 16:15