Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2020	May 31, 2019	May 31, 2020	May 31, 2019
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	$ 13,773	$ 83,078	$ 145,490	$ 348,791
Reconciling items:
Amortization of intangibles	(13,178)	(7,610)	(42,895)	(23,033)
Stock-based compensation expense and related charges	(16,882)	(14,506)	(62,214)	(47,452)
Restructuring, severance and related charges	(69,150)	(9,340)	(144,005)	(16,182)
Interest income	1,864	6,758	13,144	15,897
Interest expense	(41,873)	(50,514)	(132,967)	(139,326)
Cayey, Puerto Rico
Reconciling items:
Insurance recoveries				2,900
EMS
Reconciling items:
Restructuring, severance and related charges	(23,700)	(7,600)	(55,800)	(12,300)
DMS
Reconciling items:
Restructuring, severance and related charges	(29,300)	(0)	(69,000)	(2,100)
Reconciling items
Reconciling items:
Amortization of intangibles	(13,178)	(7,610)	(42,895)	(23,033)
Stock-based compensation expense and related charges	(16,882)	(14,506)	(62,214)	(47,452)
Restructuring, severance and related charges	(69,150)	(9,340)	(144,005)	(16,182)
Distressed customer charge	0	0	(14,963)	0
Business interruption and impairment charges, net	(4,574)	0	(4,574)	2,860
Acquisition and integration charges	(6,119)	(13,391)	(30,005)	(35,066)
Impairment on securities	0	0	(12,205)	0
Other expense (net of periodic benefit cost)	(8,399)	(14,084)	(32,673)	(39,391)
Interest income	1,864	6,758	13,144	15,897
Interest expense	(41,873)	(50,514)	(132,967)	(139,326)
Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	172,084	185,765	608,847	630,484
Operating Segments | EMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	102,372	130,869	291,902	303,618
Operating Segments | DMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	$ 69,712	$ 54,896	$ 316,945	$ 326,866