A theorem on integer arithmetic with a proof based on the recursion theory
Apoloniusz Tyszka · arXiv (Cornell University) · 2010
We prove that there exists a positive integer n and integers x_1,...,x_n such that 2^(2^(n-1))<|x_1| and for each integers y_1,...,y_n the inequality |x_1|<|y_1| implies that there exist i,j,k \in {1,...,n} with ((x_i+x_j=x_k) and (y_i+y_j eq y_k)) or ((x_i \cdot x_j=x_k) and (y_i \cdot y_j eq y_k)).