Ramanujan-Nagell equation:
> Does anyone know a recent reference (say in the last 60 years) to the
> problem of showing that 2^k-7 is a square for only 5 values of k ?
> The squares (2n+1)^2 are n = 0,1,2,5,90.
Maurice Mignotte, Une nouvelle resolution..., Rend. Sem. Fac. Sci. Univ.
Cagliari 54 (1984) 41-43, MR 87e:11048
Wells Johnson, The diophantine equation..., Amer. Math. Monthly 94 (1987)
59--62, MR 88b:11015
Gerhard Turnwald, A note on the Ramanujan-Nagell equation, in
Number-theoretic Analysis, Springer Lecture Notes 1452, 206-207,
MR 91m:11023
Edward L Cohen, On the Ramanujan-Nagell equation..., in Number Theory
(Banff, 1988) 81-92, MR 92d:11026
Peter Bundschuh, On the Diophantine equation of Ramanujan-Nagell, in
Seminar on Diophantine Approximation (Yokohama, 1987) 31-40, MR 92j:11030
A M S Ramasmay, Ramanujan's equation, J. Ramanujan Math. Soc. 7 (1992)
133-153, MR 94c:11027
Ian Stewart and David Tall, Algebraic Number Theory (Chapman & Hall, 1979).
There have also been many papers on generalizations.
I'm sure that a search of Math Reviews for the keyword Ramanujan-Nagell
would turn up many more papers than I have listed above.
Gerry Myerson (gerry@mpce.mq.edu.au)