Exponential growth

pxy3=1\large p^x - y^3 =1

Solve the equation above over integral values of x,y,px,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)(1,1,10) .

  • pp is a prime.

  • x,yx,y are positive integers.

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