Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	$ 260,738	$ 450,704	$ 373,401
Reconciling items:
Amortization of intangibles	(55,544)	(31,923)	(38,490)
Stock-based compensation expense and related charges	(83,084)	(61,346)	(98,511)
Restructuring, severance and related charges	(156,586)	(25,914)	(36,902)
Loss on securities	(48,625)	(29,632)	0
Interest income	14,559	21,460	17,813
Interest expense	(173,877)	(188,730)	(149,002)
Cayey, Puerto Rico
Reconciling items:
Insurance proceeds from Hurricane Maria		2,900	24,900
Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	864,053	876,611	768,147
EMS
Reconciling items:
Restructuring, severance and related charges	(61,900)	(21,500)	(16,300)
EMS | Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	447,284	480,047	451,149
DMS
Reconciling items:
Restructuring, severance and related charges	(75,600)	(2,600)	(16,600)
DMS | Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	416,769	396,564	316,998
Segment Reconciling Items
Reconciling items:
Amortization of intangibles	(55,544)	(31,923)	(38,490)
Stock-based compensation expense and related charges	(83,084)	(61,346)	(98,511)
Restructuring, severance and related charges	(156,586)	(25,914)	(36,902)
Distressed customer charges	(14,963)	(6,235)	(32,710)
Business interruption and impairment charges, net	(5,785)	2,860	(11,299)
Acquisition and integration charges	(32,167)	(52,697)	(8,082)
Loss on securities	(48,625)	(29,632)	0
Other expense (net of periodic benefit cost)	(47,243)	(53,750)	(37,563)
Interest income	14,559	21,460	17,813
Interest expense	$ (173,877)	$ (188,730)	$ (149,002)