Income Taxes - Provision for Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2021	Feb. 29, 2020	Feb. 28, 2021	Feb. 29, 2020
Income Tax Disclosure [Abstract]
Income before income taxes	$ 114,666	$ 103,109	$ 234,898	$ 211,850
Provision for income taxes	$ 18,023	$ 14,423	$ 37,049	$ 29,207
Effective tax rate	15.70%	14.00%	15.80%	13.80%