Consolidated Statements of Changes in Stockholders' Equity - USD ($) $ in Thousands	Total	Common Stock	Additional Paid-in Capital	Treasury Stock	Retained Earnings	Accumulated Other Comprehensive Loss
Balance, beginning of period (in shares) at Aug. 31, 2020		40,767,708
Beginning balance at Aug. 31, 2020	$ 896,375	$ 408	$ 939,067	$ (636,956)	$ 633,149	$ (39,293)
Beginning balance, treasury stock (in shares) at Aug. 31, 2020				2,737,456
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	399,590				399,590
Other comprehensive income (loss)	331					331
Common stock issued for employee stock plans (in shares)		360,877		318
Common stock issued for employee stock plans	64,073	$ 4	64,173	$ (104)
Vesting of restricted stock (in shares)		34,607		12,614
Vesting of restricted stock	$ (4,155)			$ (4,155)
Repurchase of common stock (in shares)	797,385			797,385
Repurchases of common stock	$ (264,702)			$ (264,702)
Stock-based compensation expense	45,065		45,065
Dividends declared	(120,224)				(120,224)
Balance, end of period (in shares) at Aug. 31, 2021		41,163,192
Ending balance at Aug. 31, 2021	1,016,353	$ 412	1,048,305	$ (905,917)	912,515	(38,962)
Ending balance, treasury stock (in shares) at Aug. 31, 2021				3,547,773
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	396,917				396,917
Other comprehensive income (loss)	(69,421)					(69,421)
Common stock issued for employee stock plans (in shares)		450,527		260
Common stock issued for employee stock plans	85,919	$ 5	86,042	$ (128)
Vesting of restricted stock (in shares)		39,499		14,229
Vesting of restricted stock	$ (6,031)			$ (6,031)
Repurchase of common stock (in shares)	46,200			46,200
Repurchases of common stock	$ (18,639)			$ (18,639)
Stock-based compensation expense	56,003		56,003
Dividends declared	$ (129,693)				(129,693)
Balance, end of period (in shares) at Aug. 31, 2022	38,044,756	41,653,218
Ending balance at Aug. 31, 2022	$ 1,331,408	$ 417	1,190,350	$ (930,715)	1,179,739	(108,383)
Ending balance, treasury stock (in shares) at Aug. 31, 2022	3,608,462			3,608,462
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 468,173				468,173
Other comprehensive income (loss)	21,242					21,242
Common stock issued for employee stock plans (in shares)		360,375		410
Common stock issued for employee stock plans	71,840	$ 3	72,003	$ (166)
Vesting of restricted stock (in shares)		83,035		32,034
Vesting of restricted stock	(13,544)	$ 1	(1)	$ (13,544)
Excise tax on share repurchases	$ (932)			$ (932)
Repurchase of common stock (in shares)	430,350			430,350
Repurchases of common stock	$ (176,720)			$ (176,720)
Stock-based compensation expense	62,038		62,038
Dividends declared	(142,816)				(142,816)
Other	$ (759)		(759)
Balance, end of period (in shares) at Aug. 31, 2023	38,025,372	42,096,628
Ending balance at Aug. 31, 2023	$ 1,619,930	$ 421	$ 1,323,631	$ (1,122,077)	$ 1,505,096	$ (87,141)
Ending balance, treasury stock (in shares) at Aug. 31, 2023	4,071,256			4,071,256