3 problems

A recursively enumerable set is a set of natural numbers recognizable by a Turing machine, and a finite-fold polynomial Diophantine representation of such a set is a polynomial Dio…

A recursively enumerable set is a set of natural numbers, and finite-fold polynomial Diophantine representability is the property that every recursively enumerable set admits a pol…

Let Davis's quaternary quartic be the equation associated with $d=7$ in the paper. Shanks–Wagstaff conjecture. This equation has infinitely many integer solutions. The conjecture c…