Stockholders' Equity - Narrative (Details) - USD ($) $ in Thousands	3 Months Ended
	Nov. 30, 2021	Nov. 30, 2020
Class of Stock [Line Items]
Repurchase of common stock (in shares)	46,200	131,800
Repurchases of common stock	$ 18,639	$ 43,144
Remaining authorized repurchase amount	$ 181,300
Number of shares repurchased in settlement of employee tax withholding obligations (in shares)	6,747	6,728
Value of shares repurchased in settlement of employee tax withholding obligations	$ 2,900	$ 2,100
Restricted stock units
Class of Stock [Line Items]
Restricted stock vested (in shares)	17,349	17,946
Number of shares repurchased in settlement of employee tax withholding obligations (in shares)	6,747	6,728
Value of shares repurchased in settlement of employee tax withholding obligations	$ 2,900	$ 2,100