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Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2021	Feb. 29, 2020	Feb. 28, 2021	Feb. 29, 2020
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	$ 208,538	$ 29,077	$ 493,945	$ 131,717
Reconciling items:
Amortization of intangibles	(11,639)	(13,577)	(23,094)	(29,717)
Stock-based compensation expense and related charges	(23,813)	(15,109)	(57,354)	(45,332)
Restructuring, severance and related charges	(6,626)	(29,604)	(4,911)	(74,855)
Impairment on securities	0	(12,205)	0	(12,205)
Interest income	1,655	5,336	3,536	11,280
Interest expense	(31,026)	(46,183)	(63,372)	(91,094)
Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	284,606	159,448	649,543	436,763
Operating Segments | EMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	98,117	72,501	220,095	161,855
Reconciling items:
Restructuring, severance and related charges	(2,500)	(14,700)	500	(32,100)
Operating Segments | DMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	186,489	86,947	429,448	274,908
Reconciling items:
Restructuring, severance and related charges	(4,000)	(14,500)	(5,000)	(39,700)
Reconciling items:
Reconciling items:
Amortization of intangibles	(11,639)	(13,577)	(23,094)	(29,717)
Stock-based compensation expense and related charges	(23,813)	(15,109)	(57,354)	(45,332)
Restructuring, severance and related charges	(6,626)	(29,604)	(4,911)	(74,855)
Distressed customer charge	0	0	0	(14,963)
Business interruption and impairment charges, net	806	0	806	0
Acquisition and integration charges	(1,261)	(7,752)	(3,374)	(23,886)
Impairment on securities	0	(12,205)	0	(12,205)
Other expense (net of periodic benefit cost)	(4,164)	(11,277)	(7,835)	(24,274)
Interest income	1,655	5,336	3,536	11,280
Interest expense	(31,026)	(46,183)	(63,372)	(91,094)
Other non-allocated assets
Reconciling items:
Restructuring, severance and related charges	$ (100)	$ (400)	$ (400)	$ (3,100)

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