Stockholders' Equity (Common Stock Outstanding) (Details) - USD ($)	3 Months Ended		6 Months Ended
	Feb. 29, 2020	Feb. 28, 2019	Feb. 29, 2020	Feb. 28, 2019	Sep. 30, 2019
Common stock outstanding:
Common stock outstanding, beginning balances (in shares)			153,520,380
Common stock outstanding, ending balance (in shares)	151,407,526		151,407,526
2020 Share Repurchase Program
Common stock outstanding:
Share repurchase program, amount authorized					$ 600,000,000.0
Number of shares repurchased (in shares)			4,400,000
Value of shares repurchased			$ 168,700,000
Share repurchase program, remaining amount available	$ 431,300,000		$ 431,300,000
Common Stock
Common stock outstanding:
Common stock outstanding, beginning balances (in shares)	152,300,356	157,986,896	153,520,380	164,588,172
Shares issued upon exercise of stock options (in shares)	43,069	11,348	56,999	11,348
Shares issued under employee stock purchase plan (in shares)	595,717	691,971	595,717	692,325
Vesting of restricted stock (in shares)	322,872	219,764	2,239,612	1,905,927
Purchases of treasury stock under employee stock plans (in shares)	(86,706)	(57,389)	(617,123)	(464,836)
Treasury shares purchased (in shares)	(1,767,782)	(5,974,261)	(4,388,059)	(13,854,607)
Common stock outstanding, ending balance (in shares)	151,407,526	152,878,329	151,407,526	152,878,329