Reduction of an arbitrary diophantine equation to one in 13 unknowns

A Note on Diophantine Representations

“…The sets of Mersenne-primes and Fermat-primes can be represented in six unknowns and seven variables in the Putnam-polynomial [6]. Using the methods in [7] and [15] Fermat's last theorem can be represented in 13 unknowns. Recently the Chinese mathematician Sun, Zhi-wei [20], [21] has reduced this number to 10.…”

On the Simplification and Equivalence Problems for Straight-Line Programs

“…The proofs for the unsolvable problems rely on the following result [11,12]. (The second reference contains a proof of the result for thirteen variables.…”

An NP-complete number-theoretic problem

“…m) with integer coefficients whether it has a nonnegative integer solution, i.e., nonnegative integers el,...,~n such that p(el,...,~n) = 0 (pi(~l ..... an) = 0 for 1 < i < m). Hilbert's tenth problem is undecidable for: (i) polynomials of degree 4 [14,18], (ii) polynomials in 13 unknowns [15] (it was reported in [13] that this has been reduced to 9 unknowns), and (iii) systems of quadratic polynomials [3,9].…”