Euler's sum of powers conjecture counterexample test without recursion.
Wikipedia: Euler's conjecture was disproven by L. J. Lander and T. R. Parkin in 1966 when, through a direct computer search on a CDC 6600, they found a counterexample for k = 5. A total of three primitive (that is, in which the summands do not all have a common factor) counterexamples are known:
27^5 + 84^5 + 110^5 + 133^5 = 144^5 (Lander & Parkin, 1966).
55^5 + 3183^5 + 28969^5 + 85282^5 = 85359^5 (Frye, 2004).