Earnings Per Share - Weighted Average Shares Outstanding (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021
Numerator
Net income used for calculating basic income per share	$ 74,910	$ 100,679	$ 292,495	$ 298,528
Net income used for calculating diluted income per share	$ 74,910	$ 100,679	$ 292,495	$ 298,528
Denominator
Weighted average common shares used in the calculation of basic income per share (in shares)	37,934	37,806	37,716	37,910
Common stock equivalents associated with stock-based compensation plans (in shares)	786	682	891	692
Shares used in calculation of diluted income per share (in shares)	38,720	38,488	38,607	38,602
Basic income per share (in USD per share)	$ 1.97	$ 2.66	$ 7.76	$ 7.87
Diluted income per share (in USD per share)	$ 1.93	$ 2.62	$ 7.58	$ 7.73