One Observation behind Two-Envelope Puzzles

Dov Samet, Iddo Samet, David Schmeidler
2004 The American mathematical monthly  
On a number of occasions (see [5], [4]), this MONTHLY has mentioned a problem originally due to J. C. P. Miller concerning relations (with integer coefficients) among numbers of the type arctan m, where m ≥ 1. The best-known instance is arctan(239) = 4 arctan(5) − 5 arctan(1), April 2004] NOTES
doi:10.2307/4145244 fatcat:ehialo6xzvclxjs3mhcwnhduiq