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In this a r t i c l e we show the NP-completeness of some simple number-theoretic problems. Natural simplifications of these problems invariably are known to be in P. Our research was motivated by the question whether one could study non-determini s t i c computation without loss of generality on a restricted, number theoretically significant class of nondeterministic Turing machines, the nondeterministic diophantine machines defined below [1, 2] . The results suggest this is true.doi:10.1145/800113.803627 dblp:conf/stoc/MandersA76 fatcat:sim4pz2f6ndkvmrc6vx66uur7a