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Stockholders' Equity (Common Stock Outstanding) (Details) - USD ($)
1 Months Ended 12 Months Ended
Aug. 31, 2020
Sep. 30, 2019
Aug. 31, 2020
Aug. 31, 2019
Aug. 31, 2018
Aug. 31, 2017
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Common stock outstanding, beginning balances (in shares)   153,520,380 153,520,380      
Common stock outstanding, ending balance (in shares) 150,330,358   150,330,358 153,520,380    
Share repurchase program, amount authorized   $ 600,000,000.0     $ 350,000,000.0 $ 450,000,000.0
Stock repurchase program, capital allocation framework period   2 years        
Number of shares repurchased (in shares) 6,000,000.0          
Value of shares repurchased $ 213,900,000          
Share repurchase program, remaining amount available $ 386,100,000   $ 386,100,000      
Common Stock            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Common stock outstanding, beginning balances (in shares)   153,520,380 153,520,380 164,588,172 177,727,653  
Shares issued upon exercise of stock options (in shares)     56,999 11,348 30,832  
Shares issued under employee stock purchase plan (in shares)     1,106,852 1,282,042 1,105,400  
Vesting of restricted stock (in shares)     2,259,623 1,983,261 2,727,229  
Purchases of treasury stock under employee stock plans (in shares)     (621,250) (489,836) (793,052)  
Treasury shares purchased (in shares)     (5,992,246) (13,854,607) (16,209,890)  
Common stock outstanding, ending balance (in shares) 150,330,358   150,330,358 153,520,380 164,588,172