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Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($)
$ in Thousands
3 Months Ended
Nov. 30, 2020
Nov. 30, 2019
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income $ 285,407 $ 102,640
Reconciling items:    
Amortization of intangibles (11,455) (16,140)
Stock-based compensation expense and related charges (33,541) (30,223)
Restructuring, severance and related charges 1,715 (45,251)
Interest income 1,881 5,944
Interest expense (32,346) (44,911)
EMS    
Reconciling items:    
Restructuring, severance and related charges 3,000 (17,400)
DMS    
Reconciling items:    
Restructuring, severance and related charges (1,000) (25,200)
Reconciling items:    
Reconciling items:    
Amortization of intangibles (11,455) (16,140)
Stock-based compensation expense and related charges (33,541) (30,223)
Restructuring, severance and related charges 1,715 (45,251)
Distressed customer charge 0 (14,963)
Acquisition and integration charges (2,113) (16,134)
Other expense (net of periodic benefit cost) (3,671) (12,997)
Interest income 1,881 5,944
Interest expense (32,346) (44,911)
Operating Segments    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income 364,937 277,315
Operating Segments | EMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income 121,978 89,354
Operating Segments | DMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income $ 242,959 $ 187,961