On the Number of Solutions of Diophantine Equations

Martin Davis
1972 Proceedings of the American Mathematical Society  
For any nontrivial set of cardinal numbers ^x0, it is shown that there is no algorithm for testing whether or not the number of positive integer solutions of a given polynomial Diophantine equation belongs to the set.
doi:10.2307/2037646 fatcat:hjb2ga2kzjgsdduurohhng2zxe