Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2018	Aug. 31, 2017	Aug. 31, 2016
Reconciling items:
Amortization of intangibles	$ (38,490)	$ (35,524)	$ (37,121)
Stock-based compensation expense and related charges	(98,511)	(48,544)	(58,997)
Restructuring and related charges	(36,902)	(160,395)	(11,369)
Loss on disposal of subsidiaries	0	(2,112)	0
Other expense	(37,563)	(28,448)	(8,380)
Interest income	17,813	12,525	9,128
Interest expense	(149,002)	(138,074)	(136,536)
Income before income tax	373,401	256,233	387,045
Cayey, Puerto Rico
Reconciling items:
Insurance proceeds from Hurricane Maria	24,900
Operating Segments
Reconciling items:
Income before income tax	768,147	667,003	630,320
Segment Reconciling Items
Reconciling items:
Stock-based compensation expense and related charges	(98,511)	(48,544)	(58,997)
Acquisition and integration costs	(8,082)	0	0
Distressed customer charges	(32,710)	(10,198)	0
Business interruption and impairment charges, net (1)	(11,299)	0	0
EMS
Reconciling items:
Restructuring and related charges	(16,300)	(51,300)	(10,700)
EMS | Operating Segments
Reconciling items:
Income before income tax	451,149	436,110	373,732
DMS
Reconciling items:
Restructuring and related charges	(16,600)	(82,400)	(800)
DMS | Operating Segments
Reconciling items:
Income before income tax	$ 316,998	$ 230,893	$ 256,588