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A note on a theorem of Perron
1986
Proceedings of the American Mathematical Society
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Given an infinite simple continued fraction [ao,ai, • •. ,an, ■ ■ •], let Mn denote [0,On,an_i,... ,ai] + [an4-i,an+2,.. .j. A well-known result due to Perron [1, III, 212] states: If an+2 = m, then there is a fc in {ra,ra + 1, ra + 2) for which Mfc > \/m2 + 4. In this note we give a new proof for this result and add that there is a j in {ra, ra + 1, ra + 2} for which Mj < \Ara2 + 4.
doi:10.1090/s0002-9939-1986-0831378-5
fatcat:bjurp3j5wraxrpqehqneqaws4e