Exponential-growth relation; Finite-fold Diophantine representation; Hilbert's 10th problem; Pell's equation

The Davis-Putnam-Robinson theorem showed that every partially computable m-ary function f(a_1, . . . , a_m) = c on the natural numbers can be specified by means of an exponential Diophantine formula involving, along with parameters a_1, . . . , a_m, …