Stockholders' Equity (Common Stock Outstanding) (Details) - USD ($)	3 Months Ended		9 Months Ended
	May 31, 2020	May 31, 2019	May 31, 2020	May 31, 2019	Sep. 30, 2019
Common stock outstanding:
Common stock outstanding, beginning balances (in shares)			153,520,380
Common stock outstanding, ending balance (in shares)	150,574,036		150,574,036
2020 Share Repurchase Program
Common stock outstanding:
Share repurchase program, amount authorized					$ 600,000,000.0
Number of shares repurchased (in shares)			5,200,000
Value of shares repurchased			$ 188,900,000
Share repurchase program, remaining amount available	$ 411,100,000		$ 411,100,000
Common Stock
Common stock outstanding:
Common stock outstanding, beginning balances (in shares)	151,407,526	152,878,329	153,520,380	164,588,172
Shares issued upon exercise of stock options (in shares)	0	0	56,999	11,348
Shares issued under employee stock purchase plan (in shares)	0	(215)	595,717	692,110
Vesting of restricted stock (in shares)	13,234	73,095	2,252,846	1,979,022
Purchases of treasury stock under employee stock plans (in shares)	(2,808)	(24,322)	(619,931)	(489,158)
Treasury shares purchased (in shares)	(843,916)	0	(5,231,975)	(13,854,607)
Common stock outstanding, ending balance (in shares)	150,574,036	152,926,887	150,574,036	152,926,887