Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2021	May 31, 2020	May 31, 2021	May 31, 2020
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	$ 213,295	$ 13,773	$ 707,240	$ 145,490
Reconciling items:
Amortization of intangibles	(12,066)	(13,178)	(35,160)	(42,895)
Stock-based compensation expense and related charges	(18,765)	(16,882)	(76,119)	(62,214)
Restructuring, severance and related charges	(744)	(69,150)	(5,655)	(144,005)
Interest income	1,563	1,864	5,099	13,144
Interest expense	(33,803)	(41,873)	(97,175)	(132,967)
Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	276,883	172,084	926,426	608,847
Operating Segments | EMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	137,119	97,824	357,214	259,679
Reconciling items:
Restructuring, severance and related charges	(0)	(23,700)	400	(55,800)
Operating Segments | DMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	139,764	74,260	569,212	349,168
Reconciling items:
Restructuring, severance and related charges	(600)	(29,300)	(5,500)	(69,000)
Reconciling items:
Reconciling items:
Amortization of intangibles	(12,066)	(13,178)	(35,160)	(42,895)
Stock-based compensation expense and related charges	(18,765)	(16,882)	(76,119)	(62,214)
Restructuring, severance and related charges	(744)	(69,150)	(5,655)	(144,005)
Distressed customer charge	0	0	0	(14,963)
Business interruption and impairment charges, net	0	(4,574)	806	(4,574)
Acquisition and integration charges	0	(6,119)	(3,374)	(30,005)
Gain (impairment) on securities	2,409	0	2,409	(12,205)
Other expense (net of periodic benefit cost)	(2,182)	(8,399)	(10,017)	(32,673)
Interest income	1,563	1,864	5,099	13,144
Interest expense	$ (33,803)	$ (41,873)	$ (97,175)	$ (132,967)