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Old 2020-03-22, 04:46   #5
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Aug 2006

135418 Posts

Originally Posted by enzocreti View Post
Are there infinitely many solutions to these Diophantine equation

10^n-a^3-b^3=c^2 with n, a, b, c positive integers?
It seems rather difficult to find positive integers n such that there are no positive integers a, b, and c with 10^n = a^3 + b^3 + c^2. n = 5 is an example, but there are no others up to 18.

I don't know of any modular obstructions.
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