The problem is to solve every Diophantine Equation in 3 variables. [A Diophantine Equation sets a polynomial with integer coefficients equal to 0. In the 3 variable case, P(x,y,z)=0. Solutions x,y,z must be integers; negative numbers are allowed. An example of a hard Diophantine Equation is x^3 + y^3 + z^3 - 30 = 0.] We want an algorithm that, given any such equation, reports the NUMBER of solutions (which will sometimes be zero or infinity). By the end of the year 2050, either an algorithm will be proven, or the problem will be proven undecidable. The conditions of the Claim are the same as for the Goldbach Conjecture Claim.