# Use geometrical approach

$\large\dfrac { { a }^{ 2 } }{ 2a{ b }^{ 2 } - { b }^{ 3 } + 1 } = c$

Given that $$a,b$$ and $$c$$ are positive integers satisfying the equation above. Find the value of $$a^b$$ such that it is larger than 1 and $$a+b$$ is minimized.

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