DIOPHANTINE REPRESENTATION OF ENUMERABLE PREDICATES
Ju. V. Matijasevič · Mathematics of the USSR-Izvestiya · 1971
An example is given of a diophantine relation which has exponential growth. This, together with the well-known results of Martin Davis, Hilary Putnam, and Julia Robinson, yields a proof that every enumerable predicate is diophantine. This theorem implies that Hilbert's tenth problem is algorithmically unsolvable.