idea of factorizing numbers with Gauss sums. Motivated by the questionof resources we then turn in Section 3 to exponential sums. Finally, inSection 4 we propose an NMR method to implement such exponential sums.We conclude in Section 5 by presenting a brief summary and an outlook.2. Factorization with Gauss sums: the central ideaOur factorization algorithm relies on the truncated Gauss sum