Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	3 Months Ended
Nov. 30, 2019	Nov. 30, 2018
Reconciling items:
Amortization of intangibles	$ (16,140)	$ (7,646)
Stock-based compensation expense and related charges	(30,223)	(17,249)
Restructuring and related charges	(45,251)	(6,025)
Interest income	5,944	4,379
Interest expense	(44,911)	(42,652)
Income	102,640	164,887
Cayey, Puerto Rico
Reconciling items:
Insurance recoveries		2,900
EMS
Reconciling items:
Restructuring and related charges	(17,400)	(4,400)
DMS
Reconciling items:
Restructuring and related charges	(25,200)	(1,600)
Reconciling items:
Reconciling items:
Amortization of intangibles	(16,140)	(7,646)
Stock-based compensation expense and related charges	(30,223)	(17,249)
Restructuring and related charges	(45,251)	(6,025)
Distressed customer charge	(14,963)	0
Business interruption and impairment charges, net(1)	0	2,860
Acquisition and integration charges	(16,134)	(8,890)
Other expense (net of periodic benefit cost)	(12,997)	(13,550)
Interest income	5,944	4,379
Interest expense	(44,911)	(42,652)
Operating Segments
Reconciling items:
Income	277,315	253,660
Operating Segments \| EMS
Reconciling items:
Income	104,700	84,095
Operating Segments \| DMS
Reconciling items:
Income	$ 172,615	$ 169,565

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