sometimes called the Ramanujan-Nagell equation, has any solutions other than ,
4, 5, 7, and 15 (Schroeppel 1972, Item 31; Ramanujan 2000, p. 327; OEIS A060728).
These correspond to , 3, 5, 11, and 181 (OEIS A038198).
Nagell (1948) and Skolem et al. (1959) showed there are no solutions past
,
thus establishing Ramanujan's question in the negative.
A generalization to two variables and was considered by Euler (Engel 1998, p. 126).
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