# Exponential growth

$\large p^x - y^3 =1$

Solve the equation above over integral values of $$x,y,p$$.

Details and assumptions:

• Input the answer as the sum of possible answers. As an explicit example, input 12 if the only triplet satisfying the equation is $$(1,1,10)$$ .

• $$p$$ is a prime.

• $$x,y$$ are positive integers.

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