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Old 2018-03-15, 16:10   #10
JeppeSN
 
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"Jeppe"
Jan 2016
Denmark

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Quote:
Originally Posted by VBCurtis View Post
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
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