Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 29, 2020	Feb. 28, 2019	Feb. 29, 2020	Feb. 28, 2019
Reconciling items:
Amortization of intangibles	$ (13,577)	$ (7,777)	$ (29,717)	$ (15,423)
Stock-based compensation expense and related charges	(15,109)	(15,697)	(45,332)	(32,946)
Restructuring and related charges	(29,604)	(817)	(74,855)	(6,842)
Interest income	5,336	4,760	11,280	9,139
Interest expense	(46,183)	(46,160)	(91,094)	(88,812)
Income	29,077	100,826	131,717	265,713
Cayey, Puerto Rico
Reconciling items:
Insurance recoveries				2,900
EMS
Reconciling items:
Restructuring and related charges	(14,700)	(300)	(32,100)	(4,700)
DMS
Reconciling items:
Restructuring and related charges	(14,500)	(500)	(39,700)	(2,100)
Reconciling items
Reconciling items:
Amortization of intangibles	(13,577)	(7,777)	(29,717)	(15,423)
Stock-based compensation expense and related charges	(15,109)	(15,697)	(45,332)	(32,946)
Restructuring and related charges	(29,604)	(817)	(74,855)	(6,842)
Distressed customer charge	0	0	(14,963)	0
Business interruption and impairment charges, net	0	0	0	2,860
Acquisition and integration charges	(7,752)	(12,785)	(23,886)	(21,675)
Impairment on securities	(12,205)	0	(12,205)	0
Other expense (net of periodic benefit cost)	(11,277)	(11,757)	(24,274)	(25,307)
Interest income	5,336	4,760	11,280	9,139
Interest expense	(46,183)	(46,160)	(91,094)	(88,812)
Operating Segments
Reconciling items:
Income	159,448	191,059	436,763	444,719
Operating Segments | EMS
Reconciling items:
Income	84,829	88,654	189,529	172,749
Operating Segments | DMS
Reconciling items:
Income	$ 74,619	$ 102,405	$ 247,234	$ 271,970